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Big Ideas Math: Modeling Real Life, Grade 7
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Big Ideas Math: Modeling Real Life, Grade 7 View details
2. Solving Equations Using Multiplication Or Division
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Exercise 1 Page 134

Use the Multiplication Property of Equality to eliminate the division.

x=- 2

Practice makes perfect
To solve the equation, we have to isolate x on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 9. This will eliminate the denominator of the fraction and isolate x.
x/5=- 2
MultEqn

LHS * 5=RHS* 5

x/5*5=- 2*5
FracMultDenomToNumber

a/5* 5 = a

x=- 2*5
Multiply

Multiply

x=- 10
To check that this solution is correct, let's substitute x= - 10 into the original equation and simplify.
x/9=10
Substitute

x= - 10

- 10/5? =- 2
MoveNegNumToFrac

Put minus sign in front of fraction

- 10/5? =- 2
CalcQuot

Calculate quotient

10=10 âś“
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.

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arrow_right Try It p.134-135
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Try It 2 (Page 134)
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