Exercise 17 Page 125

To find the value of x that will make the function equal to -4, we will substitute -4 for q(x) in the given function rule. Then, we can solve for x.

q(x)=1/2x-3

Substitute

q(x)= -4

-4=1/2x-3

AddEqn

LHS+3=RHS+3

-4+ 3=1/2x-3+ 3

AddTerms

Add terms

-1=1/2x

MoveRightFacToNum

a/c* b = a* b/c

-1=x/2

MultEqn

LHS * 2=RHS* 2

-1 * 2=x/2 * 2

MultPropNegOne

Multiplication Property of -1

-2=x/2 * 2

FracMultDenomToNumber

a/2* 2 = a

-2=x

RearrangeEqn

Rearrange equation

x=-2

When x=-2, the function equals -4.

Checking Our Answer

Verifying Our Solution

We can verify our solution by substituting x=-2 into the function and evaluating.

q(x)=1/2x-3

Substitute

x= -2

q( -2)=1/2( -2)-3

MultPosNeg

a(- b)=- a * b

q(-2)=-1/2 * 2-3

FracMultDenomToNumber

a/2* 2 = a

q(-2)=-1-3

SubTerm

Subtract term

q(-2)=-4

When x=-2, q(x)=-4, so our solution is correct.