Answer :
Sure! Let's solve the given equation step-by-step.
The equation to solve is:
[tex]\[4|x+5|=24\][/tex]
1. First, isolate the absolute value expression by dividing both sides of the equation by 4:
[tex]\[\frac{4|x+5|}{4} = \frac{24}{4}\][/tex]
Simplifying this, we get:
[tex]\[|x+5| = 6\][/tex]
2. To solve for [tex]\(x\)[/tex], we need to consider the two cases that arise from the definition of absolute value:
- Case 1: [tex]\(x + 5 = 6\)[/tex]
- Case 2: [tex]\(x + 5 = -6\)[/tex]
3. Let's solve these two cases separately:
- For Case 1: [tex]\(x + 5 = 6\)[/tex]
[tex]\[
x + 5 = 6 \implies x = 6 - 5 \implies x = 1
\][/tex]
- For Case 2: [tex]\(x + 5 = -6\)[/tex]
[tex]\[
x + 5 = -6 \implies x = -6 - 5 \implies x = -11
\][/tex]
Therefore, we find two solutions:
[tex]\[ x = 1 \][/tex]
[tex]\[ x = -11 \][/tex]
Hence, the correct answer is:
[tex]\[ \text{D. } x = -11 \text{ and } x = 1 \][/tex]
The equation to solve is:
[tex]\[4|x+5|=24\][/tex]
1. First, isolate the absolute value expression by dividing both sides of the equation by 4:
[tex]\[\frac{4|x+5|}{4} = \frac{24}{4}\][/tex]
Simplifying this, we get:
[tex]\[|x+5| = 6\][/tex]
2. To solve for [tex]\(x\)[/tex], we need to consider the two cases that arise from the definition of absolute value:
- Case 1: [tex]\(x + 5 = 6\)[/tex]
- Case 2: [tex]\(x + 5 = -6\)[/tex]
3. Let's solve these two cases separately:
- For Case 1: [tex]\(x + 5 = 6\)[/tex]
[tex]\[
x + 5 = 6 \implies x = 6 - 5 \implies x = 1
\][/tex]
- For Case 2: [tex]\(x + 5 = -6\)[/tex]
[tex]\[
x + 5 = -6 \implies x = -6 - 5 \implies x = -11
\][/tex]
Therefore, we find two solutions:
[tex]\[ x = 1 \][/tex]
[tex]\[ x = -11 \][/tex]
Hence, the correct answer is:
[tex]\[ \text{D. } x = -11 \text{ and } x = 1 \][/tex]