Answer :
To solve the equation [tex]\(4|x+5|+8=24\)[/tex], follow these steps:
1. Isolate the absolute value:
[tex]\[
4|x+5| + 8 = 24
\][/tex]
Subtract 8 from both sides:
[tex]\[
4|x+5| = 16
\][/tex]
2. Solve for the absolute value:
Divide both sides by 4:
[tex]\[
|x+5| = 4
\][/tex]
3. Split into two separate equations:
Since the absolute value of [tex]\(x+5\)[/tex] equals 4, [tex]\(x+5\)[/tex] could be 4 or [tex]\(-4\)[/tex]:
[tex]\[
x + 5 = 4 \quad \text{or} \quad x + 5 = -4
\][/tex]
4. Solve each equation:
- For [tex]\(x + 5 = 4\)[/tex]:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
- For [tex]\(x + 5 = -4\)[/tex]:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
5. Conclusion:
The solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{B. \, x=-1 \text{ and } x=-9}
\][/tex]
1. Isolate the absolute value:
[tex]\[
4|x+5| + 8 = 24
\][/tex]
Subtract 8 from both sides:
[tex]\[
4|x+5| = 16
\][/tex]
2. Solve for the absolute value:
Divide both sides by 4:
[tex]\[
|x+5| = 4
\][/tex]
3. Split into two separate equations:
Since the absolute value of [tex]\(x+5\)[/tex] equals 4, [tex]\(x+5\)[/tex] could be 4 or [tex]\(-4\)[/tex]:
[tex]\[
x + 5 = 4 \quad \text{or} \quad x + 5 = -4
\][/tex]
4. Solve each equation:
- For [tex]\(x + 5 = 4\)[/tex]:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
- For [tex]\(x + 5 = -4\)[/tex]:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
5. Conclusion:
The solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{B. \, x=-1 \text{ and } x=-9}
\][/tex]