Answered

Given the function [tex]\( f(x) = -5|x+1| + 3 \)[/tex], for what values of [tex]\( x \)[/tex] is [tex]\( f(x) = -12 \)[/tex]?

A. [tex]\( x = -2, x = -4 \)[/tex]
B. [tex]\( x = -2, x = 4 \)[/tex]
C. [tex]\( x = 2, x = -4 \)[/tex]
D. [tex]\( x = 2, x = 4 \)[/tex]



Answer :

GinnyAnswer
Certainly! Let's find the values of [tex]\( x \)[/tex] for which the function [tex]\( f(x) = -5|x+1| + 3 \)[/tex] equals [tex]\(-12\)[/tex].

Starting with the given equation:
[tex]\[ f(x) = -5|x+1| + 3 \][/tex]

We need to solve for [tex]\( x \)[/tex] such that:
[tex]\[ -5|x+1| + 3 = -12 \][/tex]

First, isolate the absolute value term:
[tex]\[ -5|x+1| + 3 = -12 \][/tex]
[tex]\[ -5|x+1| = -12 - 3 \][/tex]
[tex]\[ -5|x+1| = -15 \][/tex]

Divide both sides by [tex]\(-5\)[/tex]:
[tex]\[ |x+1| = 3 \][/tex]

The absolute value equation [tex]\( |x+1| = 3 \)[/tex] has two possible solutions:
[tex]\[ x+1 = 3 \][/tex]
and
[tex]\[ x+1 = -3 \][/tex]

Solving each equation individually:

1. For [tex]\( x + 1 = 3 \)[/tex]:
[tex]\[ x = 3 - 1 \][/tex]
[tex]\[ x = 2 \][/tex]

2. For [tex]\( x + 1 = -3 \)[/tex]:
[tex]\[ x = -3 - 1 \][/tex]
[tex]\[ x = -4 \][/tex]

Thus, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( f(x) = -12 \)[/tex] are:
[tex]\[ x = 2 \][/tex]
[tex]\[ x = -4 \][/tex]

Therefore, the correct answer is:
[tex]\[ x = 2, x = -4 \][/tex]

So, the values of [tex]\( x \)[/tex] are:
[tex]\[ \boxed{x = 2, x = -4} \][/tex]

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