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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 41 Page 40

Use the Zero Product Property to solve the equation.

- 1/2, - 2

Practice makes perfect

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

Solving

(8z+4)(5z+10)=0 To do so, we will use the Zero Product Property.

(8z+4)(5z+10)=0
ZeroProdProp

Use the Zero Product Property

lc8z+4=0 & (I) 5z+10=0 & (II)
SubEqn

(I): LHS-4=RHS-4

lc8z=-4 & (I) 5z+10=0 & (II)
SubEqn

(II): LHS-10=RHS-10

lc8z=-4 & (I) 5z=-10 & (II)
DivEqn

(I): .LHS /8.=.RHS /8.

lcz=- 12 & (I) 5z=-10 & (II)
DivEqn

(II): .LHS /5.=.RHS /5.

lcz=- 12 & (I) z=-2 & (II)

We found that the solutions of the equation are - 12 and - 2.

Checking

To check our answers, we will substitute them for z in the given equation. Let's start with z=0.

(8z+4)(5z+10)=0
Substitute

z= -1/2

(8( - 1/2)+4)(5( - 1/2)+10)? =0
MultPosNeg

a(- b)=- a * b

(- 4+4)(-2.5+10)? =0
AssociativePropAdd

Associative Property of Addition

(4-4)(10-2.5)? =0
DiffZero

4-4=0

(0)(10-2.5)? =0
ZeroPropMult

Zero Property of Multiplication

0=0 ✓

Since substituting and solving resulted in a true statement, we know that z=- 12 is a solution of the equation. Let's now check z=- 2.

(8z+4)(5z+10)=0
Substitute

z= - 2

(8( - 2)+4)(5( - 2)+10)? =0
MultPosNeg

a(- b)=- a * b

(- 16 + 4)(- 10+10)? =0
AssociativePropAdd

Associative Property of Addition

(4-16)(10-10)? =0
DiffZero

10-10=0

(4-16)(0)? =0
ZeroPropMult

Zero Property of Multiplication

0=0 ✓

This is also a true statement, so we know that z=-2 is a solution of the equation.

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