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

Chapter Review

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Exercise 15 Page 173

Use the Multiplication Property of Equality to eliminate the division.

w=50

Practice makes perfect

To solve the equation, we have to isolate w on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 20. This will eliminate the denominator of the fraction and isolate w.

- w/20=- 2.5

MultEqn

LHS * 20=RHS* 20

- w/20* 20=- 2.5*20

FracMultDenomToNumber

a/20* 20 = a

- w=- 2.5* 20

Multiply

- w=- 50

MultEqn

LHS * (- 1)=RHS* (- 1)

- w(- 1)=- 50(- 1)

MultNegNegOnePar

- a(- b)=a* b

w(1)=50(1)

IdPropMult

Identity Property of Multiplication

w=50

To check that this solution is correct, let's substitute w=50 into the original equation and simplify.

- w/20=- 2.5

Substitute

w= 50

- 50/20? =- 2.5

CalcQuot

Calculate quotient

- 2.5=- 2.5 ✓

Since the left-hand side and right-hand side are equal, w=50 is the correct solution.

Extra

Properties of Equality

There are four main Properties of Equality that we use when solving linear equations.

Properties of Equality
Addition Property of Equality	If a=b, then a+c=b+c.
Subtraction Property of Equality	If a=b, then a-c=b-c.
Multiplication Property of Equality	If a=b, then ac=bc.
Division Property of Equality	If a=b and c is not 0, then a/c=b/c.

In later chapters, you will learn about some more advanced Properties of Equality. As an example, there is a property for when we need to eliminate a radical or an exponent.

Power Property of Equality
If a=b, then a^m=b^m.

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 15 Page 173

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