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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 17 Page 173

Use the Division Property of Equality to eliminate the multiplication.

y=- 5

Practice makes perfect

To solve the equation, we have to isolate y on one side. Using the Division Property of Equality, we will divide both sides of the equation by 2. This will eliminate the multiplication and isolate y.

- 10=2y

.LHS /2.=.RHS /2.

- 10/2=2y/2

Rearrange equation

2y/2=- 10/2

▼

Simplify

MovePartNumRight

a* b/c=a/c* b

2/2y=- 10/2

a/a=1

1y=- 10/2

Identity Property of Multiplication

y=- 10/2

MoveNegNumToFrac

Put minus sign in front of fraction

y=-10/2

Calculate quotient

y=- 5

To check that this solution is correct, let's substitute y=- 5 into the original equation and simplify.

- 10=2y

y= - 5

- 10 ? = 2( - 5)

a(- b)=- a * b

- 10 ? = - 2(5)

Multiply

- 10=- 10 ✓

Since the left-hand side and right-hand side are equal, y=- 5 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