Reproduce EQ3 EQUATIONS AND INEQUALITIES STUDENT PACKET 3: SOLVING EQUATION 3
Name ___________________________ Period __________ Date ___________ EQ3 od ep r EQUATIONS AND INEQUALITIES STUDENT PACKET 3: SOLVING EQUATION 3 uc e STUDENT PACKET Solving Equations With Rational Coefficients • Solve multi-step algebraic equations. • Solve equations that involve non-integer values. • Justify the steps in equation solving. • Solve equations for one variable in terms of the others. 1 EQ3.2 Geometry and Number Problems Revisited • Use diagrams to organize information. • Use algebra to solve problems. 6 EQ3.3 Coin Problems • Use diagrams to organize information. • Solve mixture problems that involve money. • Use algebra to solve problems. 10 pl e: D o N ot R EQ3.1 Vocabulary, Skill Builders, and Review 17 Sa m EQ3.4 Equations and Inequalities (Student Pages) EQ3 – SP Solving Equations 3 WORD BANK Definition Example or Picture uc e Word ep r od equation N ot R numerical coefficient pl e: D o rational numbers m solution to an equation Sa variable Equations and Inequalities (Student Pages) EQ3 – SP0 Solving Equations 3 3.1 Solving Equations with Rational Coefficient SOLVING EQUATIONS WITH RATIONAL COEFFICIENTS Set (Goals) We will solve more algebraic equations using algebraic notation. We will justify the steps used to solve equations. Some equations will involve non-integer values. • Solve multi-step algebraic equations. • Solve equations that involve non-integer values. • Justify the steps in equation solving. od uc e Ready (Summary) Compute. 2. 7.8 – 9.6 ot R 1. 7.8 + 9.6 ep r Go (Warmup) 4. (-8.6) ÷ (4.3) 2 3 + 3 5 pl e: D 5. o N 3. (-8.6) • (4.3) 2 3 − 3 5 8. 3 4 1 2 - Sa m 3 1 7. - • - 4 2 6. Equations and Inequalities (Student Pages) EQ3 – SP1 Solving Equations 3 3.1 Solving Equations with Rational Coefficient SOLVING EQUATIONS MENTALLY 5.6 = x + 2.3 2. 3. 5.5 = 3 x + 2.5 4. 5. x+ x − 1.5 = 1.5 ot R -0.2 x = - 0.04 3 = 2 4 x− 8. 1 - x = 8 2 N 6. 1 x = 8 2 Sa m 7. pl e: D o 1 1 = 4 2 2 ep r od 1. uc e Solve each equation. Use mental strategies if possible. Equations and Inequalities (Student Pages) EQ3 – SP2 Solving Equations 3 3.1 Solving Equations with Rational Coefficient SOLVING EQUATIONS ALGEBRAICALLY uc e Solve each equation. Justify each step. Equation 1 x +3 = 5 2 2. 2x + ot R ep r od 1. What did you do? -2.6 = 3 x + 2.5 Sa m 3. pl e: D o N 1 5 = 2 6 Equations and Inequalities (Student Pages) EQ3 – SP3 Solving Equations 3 3.1 Solving Equations with Rational Coefficient uc e SOLVING EQUATIONS ALGEBRAICALLY (continued) Solve each equation. Justify each step. Equation What did you do? 1.6 x + 9.8 = 3.8 x + 5.4 5. 1 1 x+2 = x −6 2 4 3x − 4 1 = 2 x + 5 5 Sa m 6. pl e: D o N ot R ep r od 4. Equations and Inequalities (Student Pages) EQ3 – SP4 Solving Equations 3 3.1 Solving Equations with Rational Coefficient Solve each equation. 3. 3 x + 4 = -5 10 2. x + 2.5 = 4.6 4. 2 x + 3.6 = 3( x + 2.5) ot R ep r od 1. 2 4 3x + = 5 5 uc e PRACTICE N 1.5 x + 3 = 2( x − 2.5) 1 x+4 = x 2 8. -2.5 x + 3 = x − 4 Sa m 7. pl e: D o 5. 6. 3 5 x+ = x+ 4 6 Equations and Inequalities (Student Pages) EQ3 – SP5 Solving Equations 3 3.1 Solving Equations with Rational Coefficient SOLVING FOR ONE VARIABLE IN TERMS OF ANOTHER Solve for x: -3x = 6 2a. Solve for x: -14 + 5 + x = 20 3a. Solve for z: 8 + 2z = -28 1b. Solve for h: 2a. Solve for c: bh = A ep r od 1a. uc e You have learned to use properties of arithmetic and equality to solve equations. We will use the same properties to solve for one variable in terms of another. N ot R a + b + c = 2b Solve for W: 4b. Solve for y: 2L + 2W = 40 pl e: D o 3b. Solve for y: 12 + 2y = 30 x + 2y = -30 Sa m 4a. Equations and Inequalities (Student Pages) EQ3 – SP6 Solving Equations 3 3.2 Geometry and Number Problems Revisited uc e GEOMETRY AND NUMBER PROBLEMS REVISITED Ready (Summary) Set (Goals) Solve for x. 6x – 1 = -4(x – 6) 2. 2 3 x −2 = x +1 3 4 pl e: D o N ot R 1. ep r Go (Warmup) od • Use diagrams to organize information. • Use algebra to solve problems. We will use diagrams and algebra to solve problems that involve geometric concepts and number concepts. m Translate the word expressions into algebraic notation. Then simplify the expression. 3. The sum of a number and half of the number. Sa 4. Seven less than three times a number, minus the number. Equations and Inequalities (Student Pages) EQ3 – SP7 Solving Equations 3 3.2 Geometry and Number Problems Revisited GEOMETRY AND NUMBER PROBLEMS 1 uc e For each problem, underline what you are trying to find. Then answer questions a-d. 2. The sum of a number and 8 times that number is 1,107. What is the number? a. Define the variables using words or pictures. a. Define the variables using words or pictures. ep r ot R b. Write an equation and solve. o N b. Write an equation and solve. od 1. The perimeter of an isosceles triangle is 187 units. It has two congruent sides that are 10 less than four times the length of the third side. What is the length of each of the congruent sides? m pl e: D c. Write the solution in words. d. Check the solution. Sa d. Check the solution. c. Write the solution in words. Equations and Inequalities (Student Pages) EQ3 – SP8 Solving Equations 3 3.2 Geometry and Number Problems Revisited GEOMETRY AND NUMBER PROBLEMS 2 uc e For each problem, underline what you are trying to find. Then answer questions a-d. 2. Half of a number subtracted from twice the number is equal to 84. What is the number? a. Define the variables using words or pictures. a. Define the variables using words or pictures. b. Write an equation and solve. o N b. Write an equation and solve. ot R ep r od 1. The longer side of a parallelogram is 6 more than twice the length of the shorter side. The perimeter is 108 units. What is the length of each side? pl e: D c. Write the solution in words. e. Check the solution. Sa m e. Check the solution. c. Write the solution in words. Equations and Inequalities (Student Pages) EQ3 – SP9 Solving Equations 3 3.2 Geometry and Number Problems Revisited GEOMETRY AND NUMBER PROBLEMS 3 uc e For each problem, underline what you are trying to find. Then answer questions a-d. 1. A triangle has a perimeter of 30 units. The 2. The three angles in a triangle are second side is 3 times the length of the consecutive even numbers. Find the 1 number of degrees in each angle. first side. The third side is 5 units more od 2 than the length of the second side. What is the length of each side? ep r b. Write an equation and solve. pl e: D o N b. Write an equation and solve. a. Define the variables using words or pictures. ot R a. Define the variables using words or pictures. m c. Write the solution in words. f. Check the solution. Sa f. Check the solution. c. Write the solution in words. Equations and Inequalities (Student Pages) EQ3 – SP10 Solving Equations 3 3.3. Coin Problems Ready (Summary) Set (Goals) od • Use diagrams to organize information. • Solve mixture problems involving money. • Use algebra to solve problems. We will use pictures to solve mixture problems involving coins. Determine the number of cents in each amount. 2. $3.00 3. ot R $0.25 ep r Go (Warmup) 1. uc e COIN PROBLEMS $14.50 Determine the value of each collection in cents. 5 nickels 5. 6 dimes N 4. 8. 12 quarters and 3 dimes 2 quarters 9. 2 nickels, 3 pennies, and 14 dimes pl e: D o 7. 3 half-dollars 6. Determine the number of coins in each container 11. There are 20 coins in a jar. There are 12 nickels. The rest are dimes. How many dimes are there? 12. There are two coin jars. One contains nickels and the other contains dimes. The total number of coins is 20. There are n nickels. How many dimes are there? Sa m 10. There are 10 coins in a jar. There are 4 nickels. The rest are quarters. How many quarters are there? Equations and Inequalities (Student Pages) EQ3 – SP11 Solving Equations 3 3.3. Coin Problems COIN JAR PICTURES uc e Here is a way to record information about the contents of a coin jar. Number of coins is unknown Example: A coin jar contains 7 nickels. Example: A coin jar contains n nickels. • Type of coin • Type of coin • Number of coins • Number of coins • Value of coin • Value of coin • Value of coin jar 7 5 cents ot R 5 cents nickels ep r nickels od Number of coins is known • Value of coin jar N Use a coin jar picture to record information about each coin collection. • • Type of coin Number of coins • Number of coins Value of coin • Value of coin Value of coin jar • Value of coin jar: Sa m • 2. A coin jar contains q quarters. • Type of coin pl e: D • o 1. A coin jar contains 15 quarters. Equations and Inequalities (Student Pages) EQ3 – SP12 Solving Equations 3 3.3. Coin Problems Use a coin jar picture to record information about each coin collection. uc e COIN JAR PICTURES (continued) 4. A coin jar contains d dimes . • Type of coin • Type of coin • Number of coins • Number of coins • Value of coin • Value of coin • Value of coin jar • Value of coin jar: ot R ep r od 3. A coin jar contains 12 dimes. • • Type of coin Number of coins Think: 20 coins minus the number of nickels results in the remaining dimes Value of coin m • pl e: D o Think: n nickels N 5. There are two coin jars. One contains nickels and the other contains dimes. The total number of coins is 20. Value of coin jar Sa • Equations and Inequalities (Student Pages) EQ3 – SP13 Solving Equations 3 3.3. Coin Problems SOLVING COIN PROBLEMS 1 uc e Follow the steps to solve. A collection of 10 coins consist of all nickels and quarters. The total value of the coins is $1.90. How many of each coin are there in the collection? od a. Define the variables using words and pictures. Make a coin jar picture with the information. Include the value of the collection. (define variables using words and pictures) Make note of the total value in cents ep r Type of coin ot R Number of coins Value of coin ____________ + ____________ = ____________ pl e: D o Value of coin jar N b. Write an equation and solve it. The equation will show that the sum of the values in each coin jar equal the value of the collection. c. Write the solution in words. That is, answer the question. Sa m There are _____ nickels and _____ quarters. d. Check the solution. _____ cents + _____ cents = _____ cents Equations and Inequalities (Student Pages) EQ3 – SP14 Solving Equations 3 3.3. Coin Problems SOLVING COIN PROBLEMS 2 uc e Follow the steps to solve. A collection of 20 coins consists of all dimes and quarters. The total value of the coins is $3.80. How many of each are there in the collection? od a. Define the variables using words and pictures. ep r Type of coin Value of coin ____________ + ____________ = ___________ pl e: D o Value of coin jar N b. Write an equation and solve it. ot R Number of coins c. Write the solution in words. m There are ________________________________________________. Sa d. Check the solution. _____ cents + _____ cents = ____ cents Equations and Inequalities (Student Pages) EQ3 – SP15 Solving Equations 3 3.3. Coin Problems SOLVING COIN PROBLEMS 3 uc e Follow the steps to solve. A combination of 40 coins consists of all nickels and dimes. The total value of the coins is $3.10. How many of each coin are there In the collection? od a. Define the variables using words and pictures. ep r Type of coin Value of coin ____________ + ____________ = ___________ pl e: D o Value of coin jar N b. Write an equation and solve it. ot R Number of coins m c. Write the solution in words. Sa d. Check the solution. Equations and Inequalities (Student Pages) EQ3 – SP16 Solving Equations 3 3.3. Coin Problems COIN PROBLEM CHALLENGE N ot R ep r od uc e Solve each coin problem. 1. A collection of coins contains dimes and nickels. There are 5 times as many dimes as nickels. The value of the collection is $3.85. Find the number of dimes. Sa m pl e: D o 2. A collection of coins contains nickels, dimes, and quarters. There are 5 more nickels than dimes, and twice as many quarters as dimes. The value of the collection is $2.20. Find the number of each coin in the collection. Equations and Inequalities (Student Pages) EQ3 – SP17 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review FOCUS ON VOCABULARY pl e: D o N ot R ep r od uc e Use the word bank and vocabulary in this packet to complete the puzzle. Across Down 3 1 Twenty-five cents m 5 Quadrilateral where opposite sides are parallel Triangle with two equal sides 8 Sa 9 Statement that asserts two expressions are true Prove 11 Picture that organizes information 2 Numbers that include fractions and integers 4 Ten cents 6 The “-5” in -5x 7 Value that makes an equation true 12 Five cents Equations and Inequalities (Student Pages) EQ3 – SP18 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 1 -( x − y )2 -20 x+y 3. 5. (-x − y )2 2 6. -x + y ot R ep r 4. -20 ÷ x + y 2. od 1. -x - (-y) uc e Evaluate each expression for x = -10 and y = -20. -50 + (-60) 9. 40 – 140 8. 200 – (-200) 10. -140 – 40 12. -2(20 – 60) 14. - pl e: D o 7. N Compute mentally. -10 – 10 – (-10) 13. (-5•20) + (-4•25) m 11. 1 -8 • 2 4 Sa Solve each equation using a mental strategy. 4. -8 = 24 y Equations and Inequalities (Student Pages) 5. 1 (12 + z ) = 9 2 EQ3 – SP19 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review • • Use the variables below to write expressions that match each purchase. Then, evaluate each expression. Jewelry Sale Jewelry: $15.00 $12.75 $9.50 $30.00 ep r od Necklace……………………………....................................... Bracelet ……………………………………………………….... Earrings (pair) …………………………………………………… Ring…..………………………………...................................... uc e SKILL BUILDER 2 Let n = the cost of a necklace Let e = the cost of earrings Let b = the cost of a bracelet Let r = the cost of a ring ot R 1. Purchase 2 bracelets and 3 rings. N 2. Purchase 2 pairs of earrings, one ring, and one bracelet. Find the value of x to make the equation true. o 1.25 + x = 2.25 + 1.50 pl e: D 1. 2. 3 x = 3.75 Solve each equation. Draw pictures if needed. -5( x + 1) = 25 7. 3 x = -3 x − 6 Sa m 6. Equations and Inequalities (Student Pages) EQ3 – SP20 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 3 Guess Second even integer Third even integer Check Sum Sum = ______? ep r od First even Integer (x) and uc e 1. The sum of three consecutive even numbers is 372. What are the three numbers? x and Solution What is each number? ot R Equation Write an equation and solve it if you can. N Verify the solution using the equation. Make and sketch pl e: D o 2. The length of a rectangle is 5 less than twice its width. The perimeter is 14 feet. Find the length and width. Width Guess and Check Length Perimeter P = ______? W Sa m Write an equation and solve it. Equations and Inequalities (Student Pages) Equation and Solution How long is each side? Verify the solution using the equation EQ3 – SP21 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 4 uc e Chaz went running at the park. Use the graph to complete the table. 0 od 300 yd 1 min ep r Distance 600 yd 4 min Graph is not drawn to scale. Time Distance traveled 1. From 0 minutes to 1 minute N 2. From 1 minute to 4 minutes Average rate of speed ot R Time period 3. From 0 minutes to 4 minutes m 5. Suppose you poured water into this container at a constant rate. Sketch a graph and write one or two sentences to justify it. Sa Explain: Equations and Inequalities (Student Pages) Graph: Height of Water pl e: D o 4. In what part of the jog did Chaz run faster, the initial one minute or the last three minutes? Explain by referencing numbers and the shape of the graph. Number of Pours EQ3 – SP22 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 5 POOCH CLEANERS 4 washes for $____ uc e DOGGIE WASHERS 5 washes for $____ cost (y) # of washes (x) cost (y) 4 $32 $25 ot R # of washes (x) PC 6 $48 $0 pl e: D o N 2. Which is the better buy? Use entries in the tables or graphs to explain your reasoning. 3. Write equations to relate the number of dog washes to cost. y = _____________ PC y = _____________ m DW Sa 4. How can you determine unit rate from the equation? Equations and Inequalities (Student Pages) ep r DW od 1. Complete the tables and graphs. Assume a proportional relationship. The graph for Doggie Washers (DW) is provided. A partial table for Pooch Cleaners (PC) is provided. Use tables and graphs to complete pricing circles above. 0 5 5. Identify the coordinates when x = 1 DW (1, ____) PC (1, ____) 6. What does this represent in the context of the problem? 7. Identify the coordinates when x = 0 DW (0, ____) PC (0, ____) What does this represent in the context of the problem? EQ3 – SP23 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 6 od ep r Which train is it, and how many hours have passed? Guess Make a sketch (if needed) uc e 1. Two trains start traveling in the same direction, from the same place and at the same time. Train A travels at a rate of 90 miles per hour and Train B travels at a rate of 120 miles per hour. After some time has passed, one train is ahead by 150 miles. Total distance traveled ____=____? pl e: D o N ot R Number of hours Distance A Train Distance B Train (x) travels travels Check x Sa m Equation Write the equation and solve it. Equations and Inequalities (Student Pages) and How long will it take for one train to be ahead by 150 miles? Solution Check your answer using the equation. Which train is it? How far does each train travel? A→ B→ EQ3 – SP24 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 7 Equation/Steps -5 + 10 x = 15 x +10 What was done? given equation (nothing done) -5 + 10 x = 15 x +10 - 10 x - 10 x subtract 10x from both sides; addition (subtraction) property of equality od 1. uc e Check each solution. If it is correct, write in what was done for each step. If it is incorrect, find the mistake and correct it. Use pictures if needed. - 5 = 5 x + 10 - 10 ep r -10 -1 = x N Check solution by substitution: ot R -5 5 x = 5 5 Equation/Steps What was done? -6( x − 5) = 4 x + 20 given equation (nothing done) o 2. pl e: D -6 x − 5 = 4 x + 20 +6 x + 6x Sa m -5 = 10 x + 20 -20 - 20 -25 10 x = 10 10 -5 = x 2 Check solution by substitution: Equations and Inequalities (Student Pages) EQ3 – SP25 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 8 Equation/Steps What did you do? (include the property used) x − 2 x − 5 = 3( x + 5) given equation N Check solution by substitution: ot R ep r od 1. uc e Write all the steps used to solve the equations. Provide justifications/explanations for each step. Use pictures as needed. Equation/Steps o 2. What did you do? Sa m pl e: D − 2x = - 6 − x + 3 Check solution by substitution: Equations and Inequalities (Student Pages) EQ3 – SP26 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 9 uc e For each Problem, underline what you are trying to find. Then answer questions a-d. ep r b. Write an equation and solve. pl e: D o N b. Write an equation and solve. a. Define the variables using words or pictures. ot R a. Define the variables using words or pictures. od 1. The length of the second side of a triangle 2. The sum of three consecutive odd is 2 less than 3 times the length of the integers is -111. What are the three first side. The third side is 4 times longer numbers? than the first side. The perimeter of the triangle is 10 units. How long is each side? m c. Write the solution in words. g. Check the solution. Sa g. Check the solution. c. Write the solution in words. Equations and Inequalities (Student Pages) EQ3 – SP27 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 10 3( x + 2) = 36 2. 3. -3 x − 15 = 2 x 4. 5. -3(2 x + 1) = -5 x − 4 2( x − 6) = x − 3 ep r od 1. uc e Solve for x. 6. -20 x − 8 = -12 x + 24 Sa m pl e: D o N ot R - x + 5 = -2( x − 6) Equations and Inequalities (Student Pages) EQ3 – SP28 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 11 1 1 = 10 x − 6 5 3. 2 1 x−4 = x+8 3 6 2. 2(x – 4.5) = -2.5 + x ot R ep r od 1. uc e Solve each equation. 10.4 – 1.5x = 3.6 x – 30.4 -0.5 x + 4 = 2 x − 6 6. 1 6 x − 1 + x = 3 3 Sa m 5. pl e: D o N 4. Equations and Inequalities (Student Pages) EQ3 – SP29 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 12 Solve for t: 6t = D 2. Solve for t: x – 2y = 7 4. Solve for y: rt = D x – 2y = 7 Solve for H: LWH = V 6. Solve for B: 8. Solve for y: A= 1 Bh 2 pl e: D o 5. N ot R 3. Solve for x: ep r od 1. uc e Solve for the variable indicated. 3x + y = 12 3x + y = 12 Sa m 7. Solve for x: Equations and Inequalities (Student Pages) EQ3 – SP30 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review SKILL BUILDER 13 2x + 18 od x + 50 uc e For each problem below, the diagram shows two parallel lines cut by a transversal. Find the value of x and the value of all the angles in the diagram. 1. 2. 2x - 40 N ot R ep r 3x - 50 3. 4. pl e: D o 2x + 5 2x + 18 145 Sa m 100 Equations and Inequalities (Student Pages) EQ3 – SP31 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review Show your work on a separate sheet of paper and choose the best answer. 2. Solve for x: A. -24 B. 0 C. 2.5 x + 5 = 2( x − 3.5) B. -8 C. 1 D. 2 ep r -1 8 ot R A. 1 1 ( x − 1) = 2 2 od 1. What is the solution to the equation uc e TEST PREPARATION D. 24 14 + n = 72 C. 14 − n = 72 B. 72n = 14 D. 72 + n = 14 pl e: D o A. N 3. The sum of a number and 14 is 72. Which equation shows this relationship? 4. The sum of two numbers is 88. One number is 7 times more than the other. What is the smaller number? A. 10 B. 11 C. 70 D. 77 Sa m 5. You have a collection of 15 coins, all dimes and quarters. The total value of the coins is $2.25. How many dimes do you have? A. 10 B. Equations and Inequalities (Student Pages) 5 C. -5 D. -10 EQ3 – SP32 Solving Equations 3 3.4 Vocabulary, Skill Builders, and Review KNOWLEDGE CHECK uc e Show your work on a separate sheet of paper and write your answers on this page. 3.1 Solving Equations with Rational Coefficients 2 5 = 2x + 3 6 2. ot R 3.2 Perimeter and Number Problems Revisited 2.5 x + 7.5 = 0.5 x + 16.5 ep r x+ 1. od Solve each equation and justify each step. Solve. o N 3. Three times a number added to 5 times the same number is equal to 176. What is the number? pl e: D 4. The perimeter of a rectangle is 98 units. The length is 9 units more than the width. Find the dimensions of the rectangle. 3.3 Coin Problems m Solve. Sa 5. A collection of 13 coins consists of all nickels and dimes. The total value of the coins is $0.90. How many of each coin are there in the collection? Equations and Inequalities (Student Pages) EQ3 – SP33 Solving Equations 3 Sa m pl e: D o N ot R ep r od uc e This page is left intentionally blank for notes Equations and Inequalities (Student Pages) EQ3 – SP34 Solving Equations 3 Sa m pl e: D o N ot R ep r od uc e This page is left intentionally blank for notes. Equations and Inequalities (Student Pages) EQ3 – SP35 Solving Equations 3 Sa m pl e: D o N ot R ep r od uc e This page is left intentionally blank for notes. Equations and Inequalities (Student Pages) EQ3 – SP36 Solving Equations 3 HOME-SCHOOL CONNECTION 5 1 x + x + 11 = -1 2 2 od 1. Solve the equation uc e Here are some questions to review with your young mathematician. ot R ep r 2. The length of the second side of a triangle is five units less than the length of the first side. The length of the third side is twice the length of the first side. The perimeter of the triangle is 63 units. How long is each side? o N 3. A collection of 20 coins contains all dimes and quarters. The total value of the coins is $3.20. How many of each coin are there in the collection? Sa m pl e: D Parent (or Guardian) signature ________________________________________________ Equations and Inequalities (Student Pages) EQ3 – SP37 Solving Equations 3 COMMON CORE STATE STANDARDS – MATHEMATICS uc e SELECTED COMMON CORE STATE STANDARDS FOR MATHEMATICS Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? 8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. FIRST PRINTING ep r od 7.EE.1 DO NOT DUPLICATE © 2011 STANDARDS FOR MATHEMATICAL PRACTICE Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. MP3 MP4 MP5 Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. MP6 MP7 MP8 Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Sa m pl e: D o N ot R MP1 MP2 Equations and Inequalities (Student Pages) EQ3 – SP38
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