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Big Ideas Math: Modeling Real Life, Grade 7

BI

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

Chapter Review

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Exercise 16 Page 173

Use the Division Property of Equality to eliminate the multiplication.

x=- 2

Practice makes perfect

To solve the equation, we have to isolate x on one side. Using the Division Property of Equality, we will divide both sides of the equation by 4. This will eliminate the multiplication and isolate x.

4x=- 8

.LHS /4.=.RHS /4.

4x/4=- 8/4

MovePartNumRight

a* b/c=a/c* b

4/4x=- 8/4

a/a=1

1x=- 8/4

Identity Property of Multiplication

x=- 8/4

MoveNegNumToFrac

Put minus sign in front of fraction

x=- 8/4

Calculate quotient

x=- 2

To check that this solution is correct, let's substitute x=- 2 into the original equation and simplify.

4x=- 8

x= - 2

4( - 2)? =- 8

Multiply

- 8=- 8 ✓

Since the left-hand side and right-hand side are equal, x=- 2 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