High School

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

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

Sure! Let's solve the equation [tex]\(4|x+5|=24\)[/tex] step by step.

1. First, we need to isolate the absolute value expression. We do this by dividing both sides of the equation by 4:
[tex]\[
\frac{4|x+5|}{4} = \frac{24}{4}
\][/tex]
This simplifies to:
[tex]\[
|x+5| = 6
\][/tex]

2. The equation [tex]\( |x+5| = 6 \)[/tex] means that [tex]\( x+5 \)[/tex] can be either 6 or -6. So, we write down two separate equations to consider both possibilities:
[tex]\[
x+5 = 6 \quad \text{or} \quad x+5 = -6
\][/tex]

3. Now, let's solve each of these equations separately:

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

- For [tex]\( x+5 = -6 \)[/tex]:
[tex]\[
x + 5 = -6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -6 - 5
\][/tex]
So, we get:
[tex]\[
x = -11
\][/tex]

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

Given these solutions, the correct answer is:

A. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex]