Question

Given the function

f(x)=0.5|x-4|-3, for what values of x is f(x)=7?

A. x=-24, x=16
B. x=-16, x=24
C. x=-1, x=9
D. x=1, x=-9

Answer 1

7 = 0.5|x-4|- 3 add 3 to both sides: -
0.5|x-4| = 10 divide bs by 0,5:-
|x-4| = 20

either x - 4 = 20 or x - 4 = -20

this gives x = 24, x = -16

Answer 2

we have

`f(x)=0.5\left|x-4\right|-3` -----> equation A

`f(x)=7` -----> equation B

equate equation A and equation B

`0.5\left|x-4\right|-3=7`

Adds
`3` boths sides

`0.5\left|x-4\right|-3+3=7+3`

`0.5\left|x-4\right|=10`

Multiply by
`2` boths sides

`\left|x-4\right|=20`

we know that

The function absolute value has two solutions

Step 1

Find the first solution (positive case)

`+(x-4)=20`

Adds
`4` boths sides

`x-4+4=20+4`

`x=24`

Step 2

Find the second solution (negative case)

`-(x-4)=20`

Multiply by
`-1` boths sides

`(x-4)=-20`

Adds
`4` boths sides

`x-4+4=-20+4`

`x=-16`

therefore

the answer is the option B

`x=-16, x=24`