Given the function f(x) = 0.5|x – 4| – 3, for what values of x is f(x) = 7? x = –24, x = 16
x = –16, x = 24
x = –1, x = 9
x = 1, x = –9

x = - 16, x = 24

Step-by-step explanation:

Given f(x) = 7 then equate f(x) to 7

0.5 | x - 4 | - 3 = 7 ( add 3 to both sides )

0.5 | x - 4 | = 10 ( divide both sides by 0.5 )

| x - 4 | = 20

The expression inside the absolute value bars can be positive or negative, so

x - 4 = 20 ( add 4 to both sides )

x = 24

OR

- (x - 4) = 20

- x + 4 = 20 ( subtract 4 from both sides )

- x = 16 ( multiply both sides by - 1 )

x = - 16

-9

step-by-step explanation:

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: