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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
5. Using the Distributive Property
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Exercise 10 Page 39

Use the Zero Product Property to solve the equation.

- 0.5, 3

Practice makes perfect

We want to solve the given equation. At the end, we will check that our answer is correct.

Solving

(4m+2)(3m-9)=0 To do so, we will use the Zero Product Property.

(4m+2)(3m-9)=0
ZeroProdProp

Use the Zero Product Property

lc4m+2=0 & (I) 3m-9=0 & (II)
SubEqn

(I): LHS-2=RHS-2

lc4m=-2 & (I) 3m-9=0 & (II)
DivEqn

(I): .LHS /4.=.RHS /4.

lcm=-0.5 & (I) 3m-9=0 & (II)
AddEqn

(II): LHS+9=RHS+9

lcm=-0.5 & (I) 3m=9 & (II)
DivEqn

(II): .LHS /3.=.RHS /3.

lcm=-0.5 & (I) m=3 & (II)

We found that the solutions of the equation are - 0.5 and 3.

Checking

To check our answers, we will substitute them for m in the given equation. Let's start with m=-0.5.

(4m+2)(3m-9)=0
Substitute

m= - 0.5

(4( - 0.5)+2)(3( - 0.5)-9)? =0
MultPosNeg

a(- b)=- a * b

(- 2+2)(- 1.5-9)? =0
AssociativePropAdd

Associative Property of Addition

(2-2)(- 1.5-9)? =0
DiffZero

2-2=0

(0)(- 1.5-9)? =0
ZeroPropMult

Zero Property of Multiplication

0=0 ✓

Since substituting and solving resulted in a true statement, we know that m=- 0.5 is a solution of the equation. Let's now check m=3.

(4m+2)(3m-9)=0
Substitute

m= 3

(4( 3)+2)(3( 3)-9)? =0
Multiply

Multiply

(12+2)(9-9)? =0
DiffZero

9-9=0

(12+2)(0)? =0
ZeroPropMult

Zero Property of Multiplication

0=0 ✓

This is also a true statement, so we know that m=3 is a solution of the equation.

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Exercises 2 (Page 39)
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