Answer :
To solve the equation [tex]\(4|x+5|=24\)[/tex], follow these steps:
1. Isolate the absolute value:
[tex]\[
4|x+5| = 24
\][/tex]
Divide both sides by 4 to isolate [tex]\(|x+5|\)[/tex]:
[tex]\[
|x+5| = \frac{24}{4} = 6
\][/tex]
2. Set up two separate equations:
When dealing with an absolute value equation like [tex]\(|x + 5| = 6\)[/tex], we need to consider two cases:
- Case 1: [tex]\(x + 5 = 6\)[/tex]
- Case 2: [tex]\(x + 5 = -6\)[/tex]
3. Solve the first equation:
[tex]\[
x + 5 = 6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 6 - 5
\][/tex]
[tex]\[
x = 1
\][/tex]
4. Solve the second equation:
[tex]\[
x + 5 = -6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -6 - 5
\][/tex]
[tex]\[
x = -11
\][/tex]
5. Combine the solutions:
The solutions to the given equation are [tex]\( x = 1 \)[/tex] and [tex]\( x = -11 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex]
1. Isolate the absolute value:
[tex]\[
4|x+5| = 24
\][/tex]
Divide both sides by 4 to isolate [tex]\(|x+5|\)[/tex]:
[tex]\[
|x+5| = \frac{24}{4} = 6
\][/tex]
2. Set up two separate equations:
When dealing with an absolute value equation like [tex]\(|x + 5| = 6\)[/tex], we need to consider two cases:
- Case 1: [tex]\(x + 5 = 6\)[/tex]
- Case 2: [tex]\(x + 5 = -6\)[/tex]
3. Solve the first equation:
[tex]\[
x + 5 = 6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 6 - 5
\][/tex]
[tex]\[
x = 1
\][/tex]
4. Solve the second equation:
[tex]\[
x + 5 = -6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -6 - 5
\][/tex]
[tex]\[
x = -11
\][/tex]
5. Combine the solutions:
The solutions to the given equation are [tex]\( x = 1 \)[/tex] and [tex]\( x = -11 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( x = -11 \)[/tex] and [tex]\( x = 1 \)[/tex]