Answer :
To solve the equation [tex]\(4|x+5|=24\)[/tex], we can follow these steps:
1. Divide both sides by 4 to simplify the equation:
[tex]\[
|x+5| = 6
\][/tex]
2. Consider the definition of absolute value: The expression [tex]\(|x+5| = 6\)[/tex] means that the expression inside the absolute value, [tex]\(x+5\)[/tex], can be either 6 or -6. This leads to two separate equations:
- Equation 1:
[tex]\[
x + 5 = 6
\][/tex]
- Equation 2:
[tex]\[
x + 5 = -6
\][/tex]
3. Solve each equation for [tex]\(x\)[/tex]:
- For Equation 1:
[tex]\[
x + 5 = 6 \\
x = 6 - 5 \\
x = 1
\][/tex]
- For Equation 2:
[tex]\[
x + 5 = -6 \\
x = -6 - 5 \\
x = -11
\][/tex]
So, the solutions are [tex]\(x = 1\)[/tex] and [tex]\(x = -11\)[/tex].
Therefore, the correct option is:
D. [tex]\(x=-11\)[/tex] and [tex]\(x=1\)[/tex].
1. Divide both sides by 4 to simplify the equation:
[tex]\[
|x+5| = 6
\][/tex]
2. Consider the definition of absolute value: The expression [tex]\(|x+5| = 6\)[/tex] means that the expression inside the absolute value, [tex]\(x+5\)[/tex], can be either 6 or -6. This leads to two separate equations:
- Equation 1:
[tex]\[
x + 5 = 6
\][/tex]
- Equation 2:
[tex]\[
x + 5 = -6
\][/tex]
3. Solve each equation for [tex]\(x\)[/tex]:
- For Equation 1:
[tex]\[
x + 5 = 6 \\
x = 6 - 5 \\
x = 1
\][/tex]
- For Equation 2:
[tex]\[
x + 5 = -6 \\
x = -6 - 5 \\
x = -11
\][/tex]
So, the solutions are [tex]\(x = 1\)[/tex] and [tex]\(x = -11\)[/tex].
Therefore, the correct option is:
D. [tex]\(x=-11\)[/tex] and [tex]\(x=1\)[/tex].