Exercise 11 Page 128

To find the value of x that will make the function equal to - 3, we will substitute - 3 for w(x) into the given function rule. Then we can solve for x.

w(x)=-2x+7

Substitute

w(x)= - 3

- 3=-2x+7

SubEqn

LHS-7=RHS-7

-10=-2x

DivEqn

.LHS /(- 2).=.RHS /(- 2).

5=x

RearrangeEqn

Rearrange equation

x=5

When x=5, the function equals -3.

Checking Our Answer

Verifying Our Solution

We can verify our solution by substituting x=5 into the rule and evaluating.

w(x)=-2x+7

Substitute

x= 5

w( 5)=-2( 5)+7

Multiply

Multiply

w(5)=-10+7

AddTerms

Add terms

w(5)=- 3

When x=5, w(x)=-3, so our solution is correct.