Answer :
To solve the equation [tex]\(4|x+5| = 24\)[/tex], we start by simplifying the equation.
1. Divide both sides by 4:
[tex]\[
|x+5| = 6
\][/tex]
2. Solve the absolute value equation:
The equation [tex]\(|x + 5| = 6\)[/tex] can be split into two separate equations because absolute value expressions represent the distance from zero, which can be either positive or negative:
- Equation 1:
[tex]\[
x + 5 = 6
\][/tex]
- Equation 2:
[tex]\[
x + 5 = -6
\][/tex]
3. Solve each equation separately:
- Solve Equation 1:
[tex]\[
x + 5 = 6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 6 - 5 = 1
\][/tex]
- Solve Equation 2:
[tex]\[
x + 5 = -6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -6 - 5 = -11
\][/tex]
4. Conclusion:
The solutions are [tex]\(x = 1\)[/tex] and [tex]\(x = -11\)[/tex].
Thus, the correct answer is:
C. [tex]\(x = -11\)[/tex] and [tex]\(x = 1\)[/tex]
1. Divide both sides by 4:
[tex]\[
|x+5| = 6
\][/tex]
2. Solve the absolute value equation:
The equation [tex]\(|x + 5| = 6\)[/tex] can be split into two separate equations because absolute value expressions represent the distance from zero, which can be either positive or negative:
- Equation 1:
[tex]\[
x + 5 = 6
\][/tex]
- Equation 2:
[tex]\[
x + 5 = -6
\][/tex]
3. Solve each equation separately:
- Solve Equation 1:
[tex]\[
x + 5 = 6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 6 - 5 = 1
\][/tex]
- Solve Equation 2:
[tex]\[
x + 5 = -6
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -6 - 5 = -11
\][/tex]
4. Conclusion:
The solutions are [tex]\(x = 1\)[/tex] and [tex]\(x = -11\)[/tex].
Thus, the correct answer is:
C. [tex]\(x = -11\)[/tex] and [tex]\(x = 1\)[/tex]