Answer :
To solve the equation [tex]\(4|x+5| + 8 = 24\)[/tex], follow these steps:
1. Isolate the Absolute Value Expression:
- Start by subtracting 8 from both sides of the equation to move the constant term:
[tex]\[
4|x+5| = 16
\][/tex]
2. Simplify Further:
- Divide both sides of the equation by 4 to solve for the absolute value expression:
[tex]\[
|x+5| = 4
\][/tex]
3. Solve the Absolute Value Equation:
- The expression [tex]\(|x+5| = 4\)[/tex] means that [tex]\(x+5\)[/tex] can be 4 or -4. So, we will solve both possible equations:
- 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. Conclusion:
- The solutions to the equation [tex]\(4|x+5| + 8 = 24\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Therefore, the correct answer is option A: [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
1. Isolate the Absolute Value Expression:
- Start by subtracting 8 from both sides of the equation to move the constant term:
[tex]\[
4|x+5| = 16
\][/tex]
2. Simplify Further:
- Divide both sides of the equation by 4 to solve for the absolute value expression:
[tex]\[
|x+5| = 4
\][/tex]
3. Solve the Absolute Value Equation:
- The expression [tex]\(|x+5| = 4\)[/tex] means that [tex]\(x+5\)[/tex] can be 4 or -4. So, we will solve both possible equations:
- 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. Conclusion:
- The solutions to the equation [tex]\(4|x+5| + 8 = 24\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Therefore, the correct answer is option A: [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].