College

Solve [tex]$4|x+5|=16$[/tex]

A. [tex]$x=1$[/tex] and [tex]$x=-1$[/tex]
B. [tex]$x=1$[/tex] and [tex]$x=-9$[/tex]
C. [tex]$x=-1$[/tex] and [tex]$x=9$[/tex]
D. [tex]$x=-1$[/tex] and [tex]$x=-9$[/tex]

Answer :

Sure, let's solve the given equation step-by-step.

The equation is [tex]\(4|x+5|=16\)[/tex].

1. Isolate the absolute value expression:

[tex]\[
4|x+5| = 16
\][/tex]

Divide both sides by 4 to get:

[tex]\[
|x+5| = 4
\][/tex]

2. Solve the absolute value equation:

The equation [tex]\(|x+5| = 4\)[/tex] means that [tex]\(x+5\)[/tex] can be 4 or -4. Hence, we consider two cases:

- Case 1: [tex]\(x+5 = 4\)[/tex]
- Case 2: [tex]\(x+5 = -4\)[/tex]

3. Solve for [tex]\(x\)[/tex] in each case:

- Case 1:

[tex]\[
x+5 = 4
\][/tex]

Subtract 5 from both sides:

[tex]\[
x = 4 - 5
\][/tex]

[tex]\[
x = -1
\][/tex]

- Case 2:

[tex]\[
x+5 = -4
\][/tex]

Subtract 5 from both sides:

[tex]\[
x = -4 - 5
\][/tex]

[tex]\[
x = -9
\][/tex]

4. List possible solutions:

The solutions are [tex]\(x = -1\)[/tex] and [tex]\(x= -9\)[/tex].

So the correct answer is [tex]\( \boxed{\text{D. } x=-1 \text{ and } x=-9} \)[/tex].