Question

Given the function f(x) = 0.5|x – 4| – 3, for what values of x is f(x) = 7?

Answer 1

7=0.5 |x-4| -3
+3                +3
10=0.5 |x-4|
10/0.5=0.5/0.5 |x-4|
20=|x-4|
             ^
-20=x-4   20=x-4
 +4    +4    +4    +4
-16=x       24=x

The answers are -16=x and 24=x

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Answer 2

Remember, if a=|b| assume
a=b and -a=b

so


f(x)=7
7=0.5|x-4|-3
add 3 to both sides
10=0.5|x-4|
divide both sides by 0.5 (or times both sides by 2)
20=|x-4|
therefor

20=x-4 and -20=x-4
add 4 to both sidesr
24=x and -16=x


the values are at x=-16 and 24