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

Chapter Review

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Exercise 18 Page 173

Use the Division Property of Equality to eliminate the multiplication.

z=6

Practice makes perfect

To solve the equation, we have to isolate z on one side. Using the Division Property of Equality, we will divide both sides of the equation by - 5.4. This will eliminate the multiplication and isolate z.

- 5.4z=- 32.4

DivEqn

.LHS /(- 5.4).=.RHS /(- 5.4).

- 5.4z/- 5.4=- 32.4/- 5.4

▼

Simplify

MovePartNumRight

a* b/c=a/c* b

- 5.4/- 5.4z=- 32.4/- 5.4

QuotOne

a/a=1

1z=- 32.4/- 5.4

IdPropMult

Identity Property of Multiplication

z=- 32.4/- 5.4

DivNegNeg

- a/- b=a/b

z=32.4/5.4

CalcQuot

Calculate quotient

z=6

To check that this solution is correct, let's substitute z=6 into the original equation and simplify.

- 5.4z=- 32.4

Substitute

z= 6

- 5.4( 6)? =- 32.4

Multiply

- 32.4=- 32.4 ✓

Since the left-hand side and right-hand side are equal, z=6 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 18 Page 173

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