High School

Solve [tex]$4|x+5|=24$[/tex]

A. [tex]$x=11$[/tex] and [tex][tex]$x=-11$[/tex][/tex]

B. [tex]$x=-11$[/tex] and [tex]$x=1$[/tex]

C. [tex][tex]$x=-11$[/tex][/tex] and [tex]$x=-1$[/tex]

D. [tex]$x=11$[/tex] and [tex][tex]$x=-1$[/tex][/tex]

Answer :

To solve the equation [tex]\(4|x+5|=24\)[/tex], follow these steps:

1. Isolate the absolute value expression:
[tex]\[
4|x+5| = 24
\][/tex]
Divide both sides by 4:
[tex]\[
|x+5| = \frac{24}{4}
\][/tex]
[tex]\[
|x+5| = 6
\][/tex]

2. Set up the two cases for the absolute value:
The absolute value [tex]\( |x + 5| = 6 \)[/tex] can be broken into two separate equations:

- Case 1: [tex]\( x + 5 = 6 \)[/tex]
- Case 2: [tex]\( x + 5 = -6 \)[/tex]

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

- For Case 1: [tex]\( x + 5 = 6 \)[/tex]
Subtract 5 from both sides:
[tex]\[
x = 6 - 5
\][/tex]
[tex]\[
x = 1
\][/tex]

- For Case 2: [tex]\( x + 5 = -6 \)[/tex]
Subtract 5 from both sides:
[tex]\[
x = -6 - 5
\][/tex]
[tex]\[
x = -11
\][/tex]

4. Write the solution:
Therefore, the solutions to the equation [tex]\( 4|x + 5| = 24 \)[/tex] are:
[tex]\[
x = 1 \text{ and } x = -11
\][/tex]

Given the provided options, the correct one is:
B. [tex]\(x = -11\)[/tex] and [tex]\(x = 1\)[/tex]