given the function f(x) = 0.5|x - 4| - 3, for what values of x is f(x) = 7?\no x = -24, x = 16\no x = -16, x…

given the function f(x) = 0.5|x - 4| - 3, for what values of x is f(x) = 7?\no x = -24, x = 16\no x = -16, x = 24\no x = -1, x = 9\no x = 1, x = -9

given the function f(x) = 0.5|x - 4| - 3, for what values of x is f(x) = 7?\no x = -24, x = 16\no x = -16, x = 24\no x = -1, x = 9\no x = 1, x = -9

Answer

Explanation:

Step1: Set up the equation

Set $0.5|x - 4|-3=7$.

Step2: Isolate the absolute - value term

Add 3 to both sides of the equation: $0.5|x - 4|=7 + 3=10$. Then divide both sides by 0.5, we get $|x - 4|=\frac{10}{0.5}=20$.

Step3: Solve the absolute - value equation

Case 1: $x−4 = 20$. Solving for $x$, we add 4 to both sides: $x=20 + 4=24$. Case 2: $x−4=-20$. Solving for $x$, we add 4 to both sides: $x=-20 + 4=-16$.

Answer:

$x=-16,x = 24$