Exercise 5 Page 123

To find the value of x that will make the function equal to -1, we will substitute -1 for g(x) in the given function rule. Then, we can solve for x.

g(x)=-1/2x+3

Substitute

g(x)= -1

-1=-1/2x+3

▼

Solve for x

SubEqn

LHS-3=RHS-3

-1- 3=-1/2x+3- 3

SubTerms

Subtract terms

-4=-1/2x

MoveRightFacToNumOne

1/b* a = a/b

-4=-x/2

MultEqn

LHS * 2=RHS* 2

-4 * 2=-x/2 * 2

Multiply

Multiply

-8=-x/2 * 2

FracMultDenomToNumber

a/2* 2 = a

-8=- x

MultEqn

LHS * (-1)=RHS* (-1)

8=x

RearrangeEqn

Rearrange equation

x=8

When x=8, the function equals -1.

Checking Our Answer

Verifying Our Solution

We can verify our solution by substituting x=8 into the function and evaluating.

g(x)=-1/2x+3

Substitute

x= 8

g( 8)=-1/2( 8)+3

MoveRightFacToNumOne

1/b* a = a/b

g(8)=-8/2+3

CalcQuot

Calculate quotient

g(8)=-4+3

AddTerms

Add terms

g(8)=-1

When x=8, g(x)=-1, so our solution is correct.