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Lesson 16
A STORY OF FUNCTIONS
M1
ALGEBRA I
Lesson 16: Solving and Graphing Inequalities Joined by “And” or
“Or”
Classwork
Exercise 1
a.
Solve 𝑤𝑤 2 = 121, for 𝑤𝑤. Graph the solution on a number line.
b.
Solve 𝑤𝑤 2 < 121, for 𝑤𝑤. Graph the solution on a number line and write the solution set as a compound inequality.
c.
Solve 𝑤𝑤 2 ≥ 121 for 𝑤𝑤. Graph the solution on a number line and write the solution set as a compound inequality.
d.
Quickly solve (𝑥𝑥 + 7)2 = 121, for 𝑥𝑥. Graph the solution on a number line.
e.
Use your work from part (d) to quickly graph the solution on a number line to each inequality below.
i.
(𝑥𝑥 + 7)2 < 121
ii.
(𝑥𝑥 + 7)2 ≥ 121
Lesson 16:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Solving and Graphing Inequalities Joined by “And” or “Or”
S.88
Lesson 16
A STORY OF FUNCTIONS
M1
ALGEBRA I
Exercise 2
Consider the compound inequality −5 < 𝑥𝑥 < 4
a.
Rewrite the inequality as a compound statement of inequality.
b.
Write a sentence describing the possible values of 𝑥𝑥.
c.
Graph the solution set on the number line below.
Exercise 3
Consider the compound inequality −5 < 2𝑥𝑥 + 1 < 4.
a.
Rewrite the inequality as a compound statement of inequality.
b.
Solve each inequality for 𝑥𝑥. Then, write the solution to the compound inequality.
c.
Write a sentence describing the possible values of 𝑥𝑥.
d.
Graph the solution set on the number line below.
Lesson 16:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Solving and Graphing Inequalities Joined by “And” or “Or”
S.89
Lesson 16
A STORY OF FUNCTIONS
M1
ALGEBRA I
Exercise 4
Given 𝑥𝑥 < −3 or 𝑥𝑥 > −1
a.
What must be true in order for the compound inequality to be a true statement?
b.
Write a sentence describing the possible values of 𝑥𝑥.
c.
Graph the solution set on the number line below.
Exercise 5
Given
a.
𝑥𝑥 + 4 < 6 or 𝑥𝑥 − 1 > 3
Solve each inequality for 𝑥𝑥. Then, write the solution to the compound inequality.
b.
Write a sentence describing the possible values of 𝑥𝑥.
c.
Graph the solution set on the number line below.
Lesson 16:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Solving and Graphing Inequalities Joined by “And” or “Or”
S.90
Lesson 16
A STORY OF FUNCTIONS
M1
ALGEBRA I
Exercise 6
Solve each compound inequality for 𝑥𝑥 and graph the solution on a number line.
a.
𝑥𝑥 + 6 < 8 and 𝑥𝑥 − 1 > −1
b.
−1 ≤ 3 − 2𝑥𝑥 ≤ 10
c.
5𝑥𝑥 + 1 < 0 or 8 ≤ 𝑥𝑥 − 5
d.
10 > 3𝑥𝑥 − 2 or 𝑥𝑥 = 4
e.
𝑥𝑥 − 2 < 4 or 𝑥𝑥 − 2 > 4
f.
𝑥𝑥 − 2 ≤ 4 and 𝑥𝑥 − 2 ≥ 4
Lesson 16:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Solving and Graphing Inequalities Joined by “And” or “Or”
S.91
Lesson 16
A STORY OF FUNCTIONS
M1
ALGEBRA I
Exercise 7
Solve each compound inequality for 𝑥𝑥 and graph the solution on a number line. Pay careful attention to the inequality
symbols and the “and” or “or” statements as you work.
a.
1 + 𝑥𝑥 > −4 or 3𝑥𝑥 − 6 > −12
b.
1 + 𝑥𝑥 > −4 or 3𝑥𝑥 − 6 < −12
c.
1 + 𝑥𝑥 > 4 and 3𝑥𝑥 − 6 < −12
Lesson 16:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Solving and Graphing Inequalities Joined by “And” or “Or”
S.92
Lesson 16
A STORY OF FUNCTIONS
M1
ALGEBRA I
Problem Set
Solve each inequality for 𝑥𝑥 and graph the solution on a number line.
𝑥𝑥
1.
𝑥𝑥 − 2 < 6 or
3.
5𝑥𝑥 ≤ 21 + 2𝑥𝑥 or 3(𝑥𝑥 + 1) ≥ 24
5.
7.
9.
3
>4
𝑥𝑥+1
2.
−6 <
4.
5𝑥𝑥 + 2 ≥ 27 and 3𝑥𝑥 − 1 < 29
0 ≤ 4𝑥𝑥 − 3 ≤ 11
6.
8 ≥ −2(𝑥𝑥 − 9) ≥ −8
8.
4
< 3
2𝑥𝑥 > 8 or −2𝑥𝑥 < 4
4𝑥𝑥 + 8 > 2𝑥𝑥 − 10 or
1
3
𝑥𝑥 − 3 < 2
7 − 3𝑥𝑥 < 16 and 𝑥𝑥 + 12 < −8
10. If inequalities question 8 were joined by “and” instead of “or,” what would the solution set become?
11. If the inequalities in question 9 were joined by “or” instead of “and,” what would the solution set become?
Lesson 16:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Solving and Graphing Inequalities Joined by “And” or “Or”
S.93