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

Chapter Review

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Exercise 14 Page 173

Use the Multiplication Property of Equality to eliminate the division.

z=3

Practice makes perfect

To solve the equation, we have to isolate z on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 4. This will eliminate the denominator of the fraction and isolate z.

- z/4=- 3/4

MultEqn

LHS * 4=RHS* 4

- z/4* 4=- 3/4* 4

FracMultDenomToNumber

a/4* 4 = a

- z=- 3

MultEqn

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

- z(- 1)=- 3(- 1)

MultNegNegOnePar

- a(- b)=a* b

z(1)=3(1)

IdPropMult

Identity Property of Multiplication

z=3

To check that this solution is correct, let's substitute z=3 into the original equation and simplify.

- z/4=- 3/4

Substitute

z= 3

- 3/4=- 3/4 ✓

Since the left-hand side and right-hand side are equal, z=3 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 14 Page 173

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