1. science
2. mathematics
3. algebra

Sample Algebra 1
Lesson Cycle
Page 1
Page 2
Page 3
Page 4
Page 5
Page 6
Page 7
Page 8
Page 9
Page 10
Page 11
Teamwork Questions and Answers
Name
Team Mastery
Directions for questions 1–9: Solve the equation and justify each step.
1)
4 – 11 = 1 – 1
x
2
2) 10 =
3)
4)
–
1
x–2
5x = 1 + x
10
3 x = –2(4 + 4x)
5
5) 9 = 7 + 3
x
6) 1 – 5x = 12 – x
7) 9(2 – x) = x – 6
8) 3x + 5 – x = x
Challenge
9) Solve the equation 3 (9 – 3 1 x) = 27 – 2x and justify each step. Explain what your solution means.
5
3
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Teamwork Questions and Answers
1
Team Mastery Answer Sheet
Note: All work is possible work.
1)
4 – 11 = 1 – 1
x
2
given
4 – 11 + 11 = 1 – 1 + 11 addition property of equality
x
2
4 + 0 = 10 1
x
2
additive inverse property
4 = 10 1
x
2
additive identity property
(x)( 4 ) = (10 1 )(x)
x
2
multiplication property of equality
1(4) = 10 1 x
2
multiplicative inverse property
4 = 10 1 x
2
multiplicative identity property
( 2 )(4) = (10 1 x)( 2 )
21
2
21
multiplication property of equality
8 = 1x
21
multiplicative inverse property
8 =x
21
multiplicative identity property
2) 10 =
1
x–2
(x – 2)(10) = (
2
given
1 )(x – 2) multiplication property of equality
x–2
10x – 20 = (1)(1)
distributive property and multiplicative inverse property
10x – 20 = 1
multiplicative identity property
10x – 20 + 20 = 1 + 20
addition property of equality
10x + 0 = 21
additive inverse property
10x = 21
additive identity property
( 1 )(10x) = (21)( 1 )
10
10
multiplication property of equality
1x = 2.1
multiplicative inverse property
x = 2.1
multiplicative identity property
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Teamwork Questions and Answers
3)
–
5x = 1 + x
10
given
–
–
–
5x + x = 1 + x + x
10
addition property of equality
–
6x = 1 + 0
10
additive inverse property
–
6x = 1
10
additive identity property
–
–
–
( 1 )( 6x) = ( 1 )( 1 )
6
10
6
1x =
x=
4)
–
–
1
60
1
60
multiplication property of equality
multiplicative inverse property
multiplicative identity property
3 x = –2(4 + 4x)
5
given
3 x = –8 + –8x
5
3 x + 8x = –8 + –8x + 8x
5
distributive property
addition property of equality
83x = 8+0
5
additive inverse property
83x = 8
5
additive identity property
–
( 5 )( 43 x) = ( 8)( 5 )
43
5
43
multiplication property of equality
–
1x = 40
43
multiplicative inverse property
–
x = 40
43
multiplicative identity property
–
–
5) 9 = 7 + 3
x
given
–
–
9+ 3= 7 +3+ 3
x
addition property of equality
6= 7 +0
x
additive inverse property
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Teamwork Questions and Answers
3
6= 7
x
additive identity property
(x)(6) = ( 7 )(x)
x
multiplication property of equality
6x = 7(1)
multiplicative inverse property
6x = 7
multiplicative identity property
( 1 )(6x) = (7)( 1 )
6
6
multiplication property of equality
1x = 7
6
multiplicative inverse property
x=11
6
multiplicative identity property
6) 1 – 5x = 12 – x
given
1 – 5x + 5x = 12 – x + 5x
addition property of equality
1 + 0 = 12 + 4x
additive inverse property
1 = 12 + 4x
additive identity property
–
–
1 + 12 = 12 + 4x + 12
addition property of equality
–
11 = 0 + 4x
additive inverse property
–
11 = 4x
additive identity property
–
( 1 )( 11) = (4x)( 1 )
4
4
–
2 3 = 1x
4
multiplicative inverse property
–
23 =x
4
multiplicative identity property
7) 9(2 – x) = x – 6
4
multiplication property of equality
given
18 – 9x = x – 6
distributive property
18 – 9x + 9x = x – 6 + 9x
addition property of equality
18 – 0 = 10x – 6
additive inverse property
18 = 10x – 6
additive identity property
18 + 6 = 10x – 6 + 6
addition property of equality
24 = 10x + 0
additive inverse property
24 = 10x
additive identity property
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Teamwork Questions and Answers
( 1 )(24) = (10x)( 1 )
10
10
multiplication property of equality
24 = 1x
10
multiplicative inverse property
22=x
5
multiplicative identity property
8) 3x + 5 – x = x
–
given
–
2x + 5 + 5 = x + 5
–
2x + 0 = x + 5
additive inverse property
–
2x = x + 5
–
additive identity property
–
–
2x + x = x + 5 + x
addition property of equality
–
additive inverse property
x= 5
–
additive identity property
3 (9 – 3 1 x) = 27 – 2x
5
3
given
27 – 2x = 27 – 2x
5
distributive property
x= 5+0
9)
addition property of equality
27 – 2x + – 27 = 27 – 2x + – 27
5
5
5
0 – 2x = 21 3 – 2x
5
addition property of equality
additive inverse property
–
2x = 21 3 – 2x
5
additive identity property
–
2x + 2x = 21 3 – 2x + 2x
5
addition property of equality
0 = 21 3 + 0
5
additive inverse property
0 = 21 3
5
additive identity property
Possible explanation: This means that the equation isn’t true. 0 cannot equal 21 3 , so both sides of
5
the equation are not equal.
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Teamwork Questions and Answers
5
Quick Check
Name
–
Solve the equation 5(3 – x) = 2x and justify each step.
Level I Unit 3 Cycle 2 Lesson 5
Quick Check
PowerTeaching: i3
© 2012 Success for All Foundation
Quick Check
Name
–
Solve the equation 5(3 – x) = 2x and justify each step.
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Quick Check
Homework Problems
Name
Team Name
Team Did Not Agree On
Questions…
Team Complete?
#’s
Quick Look
Today we solved linear equations by justifying each step, showing the properties we used to keep the two
sides of the equation equal. Here’s an example!
–
Solve the equation 2(x + 3) = 1 and justify each step.
–
2(x + 3) = 1
given
–
2x + 6 = 1
–
distributive property
–
–
2x + 6 + 6 = 1 + 6
–
addition property of equality
2x + 0 = 7
additive inverse property
2x = 7
–
additive identity property
–
( 1 )(2x) = ( 7)( 1 )
2
2
multiplication property of equality
–
1x = 7
2
multiplicative inverse property
–
x= 31
2
multiplicative identity property
Directions for questions 1–6: Solve the equation and justify each step.
1)
–
4x = 16 – 26
2) 7 – 2 = 9
x
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Homework Problems
1
3) 3x – 1 = 4 – 7x
4)
5)
6)
–
14 = 2 x – 6
3
3 =5
x +1
–
4 – x = 1 (8 – x)
2
Mixed Practice
7) Solve P = 2w + 2l for w.
8) What is the multiplicative inverse of 0.03?
4
9) Find the surface area of a cube with side lengths of 3.1 × 10 cm.
10) Use the number line below to graph x ≥ 17 . Be sure to label each division on the number line.
8
Word Problem
11) Explain why justifying each step in solving an equation is a useful process.
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Homework Problems
For the Guide on the Side
Today your student explained each step he or she took in solving linear equations. You can see an
example in the Quick Look. This practice of recording the properties used at each step is not only a good
review of properties of operations, but it also helps your student reflect on a process he or she will be
using over and over again this year. It also reinforces that we keep both sides of the equation equal at
each step. This practice provides a solid basis for when your student is faced with much more complex
equations with multiple variables and exponents, for example. As long as we preserve both sides as
equal by applying the properties, the more complex equations are simple to solve as well.
Your student should be able to answer these questions about justifying solutions:
1)
Explain how you solved for x in this equation.
2)
What does this property mean, in your own words?
3)
Is there a different way you could have solved this equation? Show me.
4)
Are the two sides of this equation still equal after what you did? How do you know?
Here are some ideas to work with justifying the solutions to equations:
1)
With your student, take a look at a recipe or instructions for something that needs
assembly. Discuss the benefits of a step-by-step approach. Analyze the
recipe/instructions to evaluate how well each step is explained so that anyone following
them would have the same result. Could the steps be in a different order? Could they be
explained more simply?
2)
Use Khan Academy to review solving equations:
https://www.khanacademy.org/math/algebra/solving-linear-equations-andinequalities/why-of-algebra/v/why-we-do-the-same--thing-to-both-sides--two-stepequations
3)
Or, use Khan Academy to review solving equations with variables on both sides:
https://www.khanacademy.org/math/algebra/solving-linear-equations-andinequalities/why-of-algebra/v/why-we-do-the-same--thing-to-both-sides-multi-stepequations
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Homework Problems
3
Homework Answers
Note: All work shown for problems 1–6 is possible work.
1)
–
4x = 16 – 26
–
4x = 10
–
addition
–
–
–
–
( 1 )( 4x) = ( 10)( 1 )
4
4
multiplication property of equality
1x = 10
4
multiplicative inverse property
x=21
2
multiplicative identity property
2) 7 – 2 = 9
x
given
–
–
7– 2 + 7=9+ 7
x
addition property of equality
0– 2 =2
x
additive inverse property
–
2 =2
x
additive identity property
–
–
–
( x)( 2 ) = (2)( x)
x
–
(1)(2) = 2x
–
multiplication property of equality
multiplicative inverse property
2 = 2x
multiplicative identity property
–
–
–
( 1 )(2) = ( 2x)( 1 )
2
2
multiplication property of equality
–
1 = 1x
multiplicative inverse property
–
1=x
multiplicative identity property
3) 3x – 1 = 4 – 7x
4
given
given
3x –1 + 7x = 4 – 7x + 7x
addition property of equality
10x – 1 = 4 + 0
additive inverse property
10x – 1 = 4
additive identity property
10x – 1 + 1 = 4 + 1
addition property of equality
10x + 0 = 5
additive inverse property
10x = 5
additive identity property
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Homework Problems
4)
( 1 )(10x) = (5)( 1 )
10
10
multiplication property of equality
1x = 1
2
multiplicative inverse property
x= 1
2
multiplicative identity property
–
14 = 2 x – 6
3
given
–
14 + 6 = 2 x – 6 + 6
3
addition property of equality
–
8= 2x+0
3
additive inverse property
–
8= 2x
3
additive identity property
–
( 3 )( 8) = ( 2 x )( 3 )
2
2
3
24 = 1x
2
multiplicative inverse property
12 = x
multiplicative identity property
3 =5
x +1
given
–
–
5)
(x + 1)(
3 ) = (5)(x + 1)
x +1
multiplication property of equality
(1)(3) = (5)(x + 1)
multiplicative inverse property
3 = 5(x + 1)
multiplicative identity property
3 = 5x + 5
distributive property
–
–
3 + 5 = 5x + 5 + 5
addition property of equality
–
2 = 5x + 0
additive inverse property
–
2 = 5x
additive identity property
–
( 1 )( 2) = (5x)( 1 )
5
5
6)
multiplicative property of equality
multiplication property of equality
–
2 = 1x
5
multiplicative inverse property
–
2 =x
5
multiplicative identity property
4 – x = 1 (8 – x)
2
given
–
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Homework Problems
5
–
4–x=4– 1x
2
distributive property
–
4–x+x=4– 1x+x
2
addition property of equality
–
4+0=4+ 1x
2
additive inverse property
–
4=4+ 1x
2
additive identity property
–
–
–
4+ 4=4+ 1x+ 4
2
addition property of equality
–
8= 1x+0
2
additive inverse property
–
8= 1x
2
additive identity property
–
(2)( 8) = ( 1 x)(2)
2
multiplication property of equality
–
16 = 1x
multiplicative inverse property
–
16 = x
multiplicative identity property
Mixed Practice
7) w = P – 2l
2
8)
100
3
9
9) 5.766 × 10 cm
2
10) Possible graph:
Word Problem
11) Possible explanation: It’s useful to explain each step in solving an equation so you remember that you
are doing the same thing to both sides at each step. This way you can see that the two sides of the
equation stay equal all the way throughout.
6
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 5
Homework Problems
Page 1
Page 2
Page 3
Page 4
Page 5
Page 6
Page 7
Page 8
Page 9
Page 10
Teamwork Questions and Answers
Name
Team Mastery
Directions for questions 1–10: Solve for x.
1)
ax + 2 = bx – 7 – ax
x
–
2) 3 – x = 2 (3 – x)
5
3) 32 = 2
x–1
4) 5
x
=
1
125
5)
a –4= 1
x
20
6)
1 (8 – 3x) = 3 – 5x – 6
2
7)
3x + 2 = 4
a
8) 0.5x + 4 + bx = 0
9) b(7 – x) = a(2 – x)
10) 81 = 3
x+7
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 6
Teamwork Questions and Answers
1
Challenge
–
11) Solve for x. Then find possible values for a and b when x = 1.
4 – bx – 5 = 3(ax + 4)
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 6
Teamwork Questions and Answers
Team Mastery Answer Sheet
1) x =
a +9
b–a
2) x = 3
3) x = 5
–
4) x = 2
5) x = 20 a
81
–
6) x = 2
7) x = 2 a
3
8) x =
–
4
0.5 + b
9) x = 7–b – 2a
a+b
–
10) x = 3
–
11) x =
3 ; possible values: a = 2, b = –3
3a + b
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 6
Teamwork Questions and Answers
3
Quick Check
Name
Solve for x in terms of a.
ax – 2 = 9
x
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 6
Quick Check
Quick Check
Name
Solve for x in terms of a.
ax – 2 = 9
x
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 6
Quick Check
Homework Problems
Name
Team Name
Team Did Not Agree On
Questions…
Team Complete?
#’s
Quick Look
Today we practiced solving more complex linear equations. Here is an example!
Solve for x in terms of a.
9(x – 3) = 5 – ax
We used the properties to rearrange the equation so the variable we need to solve for is on one side of
the equation.
9x – 27 = 5 – ax
9x – 27 + 27 = 5 – ax + 27
9x + 0 = 32 – ax
9x = 32 – ax
9x + ax = 32 – ax + ax
9x + ax = 32 + 0
9x + ax = 32
At this point, we can use the distributive property to factor out x from both addends on the left. Then we
continue to solve for x.
x(9 + a) = 32
1 [x(9 + a)] = (32) 1
9+a
9+a
1x =
x=
32
9+a
32
9+a
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 6
Homework Problems
1
Directions for questions 1–7: Solve for x.
1) 9 = 3
x
2) 3x + 8 = 9 – x + 1
3) ax + 7 = 3 – bx + ax
x+2
4) 4
= 64
5) 5 – ax = x + 2
6) 1 – b = 11
x
7) 16 = 2 – x
a
Mixed Practice
–
8) Solve the equation 1 x = 15 and justify each step.
3
9) Train A travels 210 miles in x hours. Its speed is half of Train B, whose speed is 88 miles per hour.
Solve for x.
10) This year, Mr. McGill’s school has 835 students. Last year, it had 913 students. By what percent did
the enrollment decrease?
11) A model drawing of a painting has a length of 5.25 inches and a width of 8 inches. The actual drawing
has a length of 3 feet. What is the width of the actual painting?
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 6
Homework Problems
Word Problem
12) Solve. 3
x+2
= 1 . Explain your thinking.
9
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 6
Homework Problems
3
For the Guide on the Side
Today your student practiced solving more complex linear equations for a single variable. Your student
used what he or she knows about the properties to solve equations. Your student also used his or her
knowledge of working with variables and exponents to solve more complex equations. This will prepare
him or her to find solutions to inequalities in the next lesson.
Your student should be able to answer these questions about solving equations for a single variable
1)
Explain how you solved for x in this situation. What properties helped you?
2)
How did you keep the equation balanced while you were solving for x?
3)
Will there be variables in your solution? How do you know?
4)
How can you check your work?
5)
Is there a different way you could have solved this equation? Show me.
Here are some ideas to work with justifying the solutions to equations:
4
1)
Use Khan Academy to review solving equations with the distributive property:
https://www.khanacademy.org/math/algebra/solving-linear-equations-andinequalities/complicated_equations/v/solving-equations-with-the-distributive-property
2)
Use Khan Academy to review solving equations with variables on both sides:
https://www.khanacademy.org/math/algebra/solving-linear-equations-andinequalities/basic-equation-practice/v/solving-equations-2
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 6
Homework Problems
Homework Answers
1) x = 2
2) x = 1
2
–
3) x = 4
b
4) x = 1
5) x =
6) x =
3
1+ a
–
b
10
–
7) x = 16a + 2
Mixed Practice
8)
–
1 x = 15
3
–
–
–
( 3 )( 1 x) = 15( 3 )
1
3
1
–
(1)(x) = 45
–
x = 45
given
multiplication property of equality
multiplication inverse property
multiplication identity property
9) x = 4.77
10) The enrollment decreased by 9.3%.
11) The width of the actual painting is 4.6 feet long.
Word Problem
–
12) x = 2
–2
Possible explanation: I know that 1 = 3 because of the properties of exponents. That means that x +
9
–
–
–
–
2 has to be equal to 2. 4 + 2 = 2, so x must be 2.
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 6
Homework Problems
5
Page 1
Page 2
Page 3
Page 4
Page 5
Page 6
Page 7
Page 8
Page 9
Page 10
Page 11
Teamwork Questions and Answers
Name
Team Mastery
1) Solve for x and graph the solution.
9(x – 2) < 4 – 2x
2) Dontay needs to buy 64 ounces of pasta plus a jar of his favorite spaghetti sauce. The sauce is
$5.39. His budget is $15. Write an inequality for this situation. Solve the inequality to find the greatest
cost per ounce of pasta Dontay can buy.
3) Solve for x and graph the solution.
–
9 – 2x ≥ 11
4) Solve for x and graph the solution.
–
4x > 13 – 9
5) Solve for x and graph the solution.
5 – 2x ≤ x – 1
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 7
Teamwork Questions and Answers
1
6) Rita and Linda each earn a $5-an-hour wage as servers at a restaurant, and they split the tips they
earn. For their upcoming 7-hour Saturday shift, Rita and Linda want to each earn at least $120. Write
an inequality for this situation. Solve the inequality to find the least amount of tips per hour they need
to earn to meet their goal.
7) Solve for x and graph the solution.
–
x ≥ 3(x – 8)
8) Solve for x and graph the solution.
–
x + 7 ≤ 3(1 + x)
Challenge
9) Is there a solution to this inequality? If so, what could it be?
7(x – 13) < 51 < 9x + 11
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 7
Teamwork Questions and Answers
Team Mastery Answer Sheet
1) x < 2
2) 64x + 5.39 < 15, x < about $0.15, so he should spend no more than $0.15 per ounce of pasta.
3) x ≤ 10
–
4) x < 1
5) x ≥ 2
6) 7(5 + x) ≥ 120, x ≥ about 12.15, so each has to earn at least $12.15 in tips each hour to meet
the goal.
7) x ≤ 6
–
8) x ≤ 2.5
9) Yes, there can be a solution. For example, x could be 5. It could also be 10. But it couldn’t be less
than 5, and it couldn’t be 21 or greater.
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 7
Teamwork Questions and Answers
3
Quick Check
Name
Solve for x and graph the solution.
3 – 5x ≤ 9 – x
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 7
Quick Check
Quick Check
Name
Solve for x and graph the solution.
3 – 5x ≤ 9 – x
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 7
Quick Check
Homework Problems
Name
Team Name
Team Did Not Agree On
Questions…
Team Complete?
#’s
Quick Look
Today we practiced solving inequalities in one variable. Solving an inequality simply means finding the
solution set for the variable that makes the inequality true. That is, we isolate the variable on one side of
the inequality. Here’s an example!
–
4(x – 5) ≥ x
We use the properties we know to simplify the expressions on each side and combine terms to get x on
one side.
–
4x – 20 ≥ x
–
4x – 20 – 4x ≥ x – 4x
–
0 – 20 ≥ 5x
–
–
20 ≥ 5x
–
–
–
–
( 1 )( 20) ≥ ( 5x)( 1 )
5
5
4 ≤ 1x
4≤x
Notice that when we multiply or divide both sides of an inequality by a negative number, we have to
–
switch the sign. Why? Think about how 3 < 8 is a true statement, but multiplying both sides by 1 makes
it untrue.
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 7
Homework Problems
1
1) Solve for x and graph the solution.
2 – x < 7(1 + x)
2) Solve for x and graph the solution.
5 – 3x ≥ 1 – x
3) Jackson needs to buy 3 chew toys for her 3 dogs. They have to be exactly the same toys because
her dogs are very particular. Her budget is $28. Sales tax in Jackson’s city is 5%. Write an inequality
for this situation. Solve the inequality to find the highest-priced chew toy she can buy.
4) Solve for x and graph the solution.
–
2x ≥ 7 – x
5) Solve for x and graph the solution.
4(x + 3) > 2 – x
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 7
Homework Problems
6) Solve for x and graph the solution.
1x≥6–x
2
Mixed Practice
7) Solve for x.
6 – ax = 4 + bx
8) If a car travels 199.5 miles in 3.5 hours, what is its average speed?
–
–
9) Solve 17 – 14.
10) Find the circumference of a circle with a radius of 9 inches. (Use 3.14 for π.)
Word Problem
11) Explain how solving linear inequalities is similar to and different from solving linear equations.
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 7
Homework Problems
3
For the Guide on the Side
Today your student solved inequalities in one variable, like 11 – 2x > 4x. Solving inequalities is very
similar to solving equations, except you must remember an important rule about multiplying or dividing
with negative numbers. You can see an example in the Quick Look. Practice solving inequalities is
helping prepare your student for more complex algebra later on this year. The work your student has
done in this cycle should reinforce that complex equations and inequalities can be simplified and
represented by a simple graph or solution set.
Your student should be able to answer the following questions about solving inequalities.
1) Explain how you solved this inequality.
2) Why did you switch the direction of the sign?
3) Does your answer make sense? How do you know?
4) How would your solution be different if this were an equation and not an inequality?
To help your student practice solving inequalities you might like to:
1) Represent everyday situations with inequalities. For example, perhaps you’ve budgeted that your
monthly food bill should not go above a certain number. Write an inequality with your student that
represents this situation and together consider which costs are variable each month and which
are fairly stable.
2) Watch a Khan Academy video about solving inequalities.
https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-usingmultiplication-and-division
3) Watch another Khan Academy video about solving inequalities.
https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/multi-stepinequalities
4
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 7
Homework Problems
Homework Answers
–
1) x > 5
8
2) x ≤ 2
3) 3x + 0.05(3x) < 28, x < 8.89, so she has to choose a toy that is less than $8.89.
4) x ≤ -7
5) x > –2
6) x ≥ 4
Mixed Practice
7) x =
2
b +a
8) Its average speed is 57 miles per hour.
9)
–
3
10) 56.52 inches
Word Problem
11) Possible explanation: We use the same properties to solve for x no matter whether we’re solving an
equation or an inequality. But with an inequality, we aren’t keeping both sides equal; we are keeping
the same unequal relationship. One side, for example, is greater than the other. So if we multiply both
sides by a negative number, we have to change the sign because that multiplication switched which
side was greater.
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lesson 7
Homework Problems
5
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Page 2
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Page 5
Page 6
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Page 9
Unit Check
Name
1) Joel is building a tower with blocks of two different sizes. He uses 20 blocks that have a side length of
a. He uses 15 blocks that have a side length three times larger than a. Write an equation to represent
the volume of the tower of blocks.
2) Kat works as a copyeditor. She earns a base wage of $7 per hour, plus an extra $0.55 for each page
she edits.
a. Write an equation to represent Kat’s hourly pay.
b. Use the equation to find Kat’s earnings for working 12 hours to edit a 400-page manuscript.
3) Manuel cooked brunch for a large party. His quiche recipe uses 8 eggs and 1 cup of cheese. His
squash casserole recipe uses 2 eggs and 1 cup of cheese. Manuel used 64 eggs and 11 cups of
cheese to make quiches and casseroles for the party. How many of each recipe did he make? Show
your work.
4) The figure below includes a square with height h and a rectangle with height h and length b. The area
of this figure is 20 square units. Write an equation that solves for h, the height, in terms of b.
–
5) Solve the equation 2x = 1 + 4x and justify each step.
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© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lessons 1–7
Unit Check
1
6) Solve for x.
3(bx – 4) = 3 – x
7) Solve for x.
x+4
3
= 81
8) Solve for x and graph the solution.
6 – 3x ≥ 8 – x
2
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lessons 1–7
Unit Check
Assessment Answers
Lesson 1: Create equations and inequalities in one variable to solve problems.
3
3
1) Possible equation: 20a + 15(3a ) = V, or V = 65a
3
Lesson 2: Create equations in two or more variables to solve problems.
2) a. w = 7h + 0.55p, where h = hours and p = pages edited
b. w = $304
Lesson 3: Represent constraints with equations and interpret the solution.
3) Manuel made 7 quiches and 4 squash casseroles.
Possible work: 11 = s + q; 64 = 2s + 8q
s = 11 – q; 64 = 2(11 – q) + 8q
64 = 22 – 2q + 8q
64 = 22 + 6q
42 = 6q
7=q
11 = s + 7, so s = 4
Lesson 4: Rearrange formulas to solve for a given quantity.
4) h =
20 + b 2 – b
Lesson 5: Explain each step in solving an equation.
5)
2x = 1 + 4x
8
–
2x – 4x = 1 + 4x – 4x
8
–
6x = 1 + 0
8
–
6x = 1
8
– 1 –
–
( 6x) = 1 ( 1 )
6
8 6
–
1x = 1
48
– 1
x=
48
–
given
addition property of equality
additive inverse property
additive identity property
multiplication property of equality
multiplicative inverse property
multiplicative identity property
Lesson 6: Solve equations in one variable.
6) x = 5 + 15
b
7) x = 0
Lesson 7: Solve inequalities in one variable.
8) x ≤ -1
PowerTeaching: i3
© 2012 Success for All Foundation
Level I Unit 3 Cycle 2 Lessons 1–7
Unit Check
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