Answer:
x = -4, 1
Step-by-step explanation:
Since we have a absolute value function here, we can tell there is goning to be multiple values.
First we will find x with the original function since we know |5| = 5.
Given f(x) = 5 = -2x-3,
[tex]2x-3 = 5 \\
-2x-3+3 = 5 + 3 \\
-2x = 8 \\
x = \frac{8}{ - 2} \\ = - 4[/tex]
Now we also know that |-5| = 5 as well (absolute value)
Given |-2x-3| = |-5|,
[tex] - 2x - 3 = - 5 \\ - 2x - 3 + 3 = - 5 + 3\\ - 2x = - 2 \\ x = \frac{ - 2}{ - 2} \\ = 1[/tex]
You can verifiy these 2 values by substituting them into the equation.
f(-4) = |-2(-4)-3|
= |8-3|
= |5|
= 5
f(1) = |-2(1)-3|
= |-2-3|
= |-5|
= 5
