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Big Ideas Math: Modeling Real Life, Grade 7 View details

Chapter Review

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Exercise 27 Page 174

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

w=- 8/9

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the left- and right-hand sides of the equation.

3(3w-4)=- 20

Distr

Distribute 3

3(3w)-3(4)=- 20

Multiply

9w-12=- 20

Now, we can continue to solve using the Properties of Equality.

9w-12=- 20

AddEqn

LHS+12=RHS+12

9w-12+12=- 20+12

AddTerms

Add terms

9w=- 8

DivEqn

.LHS /9.=.RHS /9.

9w/9=- 8/9

CalcQuot

Calculate quotient

w=- 8/9

MoveNegNumToFrac

Put minus sign in front of fraction

w=- 8/9

The solution to the equation is w=- 89. We can check our solution by substituting it into the original equation.

3(3w-4)=- 20

Substitute

w= - 89

3(3( - 8/9)-4) ? = - 20

▼

Simplify

MultPosNeg

a(- b)=- a * b

3(- 3(8/9)-4)? =- 20

MoveLeftFacToNum

a*b/c= a* b/c

3(- 3(8)/9-4)? =- 20

Multiply

3(- 24/9-4)? =- 20

NumberToFrac

a = 9* a/9

3(- 24/9-4(9)/9)? =- 20

Multiply

3(- 24/9-36/9)? =- 20

SubFrac

Subtract fractions

3(- 24-36/9)? =- 20

SubTerm

Subtract term

3(- 60/9)? =- 20

MoveLeftFacToNum

a*b/c= a* b/c

3(- 60)/9? =- 20

MultPosNeg

a(- b)=- a * b

- 3(60)/9? =- 20

Multiply

- 180/9? =- 20

CalcQuot

Calculate quotient

- 20=- 20

Since the left-hand side is equal to the right-hand side, our solution is correct.

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Learn More!

Are you having trouble learning how to solve equations? Would you like to see why the Properties of Equality work? Do real-world examples help you understand more about the why and how of math topics? If you answered Yes to any of these questions, check out the Mathleaks courses related to this topic!

Subchapter links

1 Solving Equations Using Addition or Subtraction p.173

2 Solving Equations Using Multiplication or Division p.173

3 Solving Two-Step Equations p.174

4 Writing and Graphing Inequalities p.174

5 Solving Inequalities Using Addition or Subtraction p.174-175

6 Solving Inequalities Using Multiplication or Division p.175

7 Solving Two-Step Inequalities p.175

Exercise 27 Page 174

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