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

1 Answer
Dec 13, 2016

#x = 24# and #x = -16#

Explanation:

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#