Given the function $f(x)= 0.5abs(x -4)-3$ , for what values x is f(x)=7?

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Answer 1 · 2016-12-13T04:56:23

$x = 24$ and $x = -16$

Given $f(x) = 0.5abs(x - 4) - 3$ and $f(x) = 7$ we can write:

$0.5abs(x - 4) - 3 = 7$

Now, we must isolate the absolute value term while keeping the equation balanced:

$0.5abs(x - 4) - 3 + 3 = 7 + 3$

$0.5abs(x - 4) - 0 = 10$

$0.5abs(x - 4) = 10$

$(0.5abs(x - 4))/0.5 = 10/0.5$

$(cancel(0.5)abs(x - 4))/cancel(0.5) = 20$

$abs(x - 4) = 20$

Because the absolute value function converts any number to a positive number we must solve the term within the absolute value for both 20 and -20:

$x - 4 = 20$

$x - 4 + 4 = 20 + 4$

$x - 0 = 24$

$x = 24$

and

$x - 4 = -20$

$x - 4 + 4 = -20 + 4$

$x - 0 = -16$

$x = -16$

Given the function f(x)= 0.5abs(x -4)-3f(x)= 0.5abs(x -4)-3, for what values x is f(x)=7?