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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 42 Page 40

Use the Zero Product Property to solve the equation.

- 3/7, 3

Practice makes perfect

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

Solving

(7x+3)(2x-6)=0 To do so, we will use the Zero Product Property.

(7x+3)(2x-6)=0
ZeroProdProp

Use the Zero Product Property

lc7x+3=0 & (I) 2x-6=0 & (II)
SubEqn

(I): LHS-3=RHS-3

lc7x=- 3 & (I) 2x-6=0 & (II)
AddEqn

(II): LHS+6=RHS+6

lc7x=- 3 & (I) 2x=6 & (II)
DivEqn

(I): .LHS /7.=.RHS /7.

lcx=- 37 & (I) 2x=6 & (II)
DivEqn

(II): .LHS /2.=.RHS /2.

lcx=- 37 & (I) x=3 & (II)

We found that the solutions of the equation are - 37 and 3.

Checking

To check our answers, we will substitute them for x in the given equation. Let's start with x=- 37.

(7x+3)(2x-6)=0
Substitute

x= -3/7

(7( - 3/7)+3)(2( - 3/7)-6)? =0
MultPosNeg

a(- b)=- a * b

(- 3+3)(-6/7-6)? =0
AssociativePropAdd

Associative Property of Addition

(3-3)(6-6/7)? =0
DiffZero

3-3=0

(0)(6-6/7)? =0
ZeroPropMult

Zero Property of Multiplication

0=0 ✓

Since substituting and solving resulted in a true statement, we know that x=- 37 is a solution of the equation. Let's now check x=3.

(7x+3)(2x-6)=0
Substitute

x= 3

(7( 3)+3)(2( 3)-6)? =0
Multiply

Multiply

(21 + 3)(6-6)? =0
DiffZero

6-6=0

(21 + 3)(0)? =0
ZeroPropMult

Zero Property of Multiplication

0=0 ✓

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

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