Question

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

Answer 1

Answer:

x = -16 or x = 24

Step-by-step explanation:

$f(x)=0.5|x-4|-3\\\\f(x)=7\Rightarrow0.5|x-4|-3=7\qquad\text{add 3 to both sides}\\\\0.5|x-4|=10\qquad\text{multiply both sides by 2}\\\\|x-4|=20\iff x-4=\pm20\\\\x-4=-20\qquad\text{add 4 to both sides}\\x=-16\\\\x-4=20\qquad\text{add 4 to both sides}\\x=24$

Answer 2

Answer: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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Step-by-step explanation: