Exercise 11 Page 165

To find the value of x that will make the function equal to 19, we will substitute 19 for r(x) in the given function rule. Then, we can solve for x.

r(x)=-5x-1

Substitute

r(x)= 19

19=-5x-1

AddEqn

LHS+1=RHS+1

20=-5x

DivEqn

.LHS /(-5).=.RHS /(-5).

-4=x

RearrangeEqn

Rearrange equation

x=-4

When x=-4, the function equals 19.

Checking Our Answer

Verifying Our Solution

We can verify our solution by substituting x=-4 into the function and evaluating.

r(x)=-5x-1

Substitute

x= -4

r( -4)=-5( -4)-1

Multiply

Multiply

r(-4)=20-1

AddTerms

Add terms

r(-4)=19

When x=-4, r(x)=19, so our solution is correct.