Answer :
Sure, let's solve the equation step by step:
Given the equation:
[tex]\[ 4|x+7| + 8 = 32 \][/tex]
1. First, isolate the absolute value term by subtracting 8 from both sides:
[tex]\[ 4|x+7| + 8 - 8 = 32 - 8 \][/tex]
[tex]\[ 4|x+7| = 24 \][/tex]
2. Next, divide both sides by 4 to further isolate the absolute value:
[tex]\[ \frac{4|x+7|}{4} = \frac{24}{4} \][/tex]
[tex]\[ |x+7| = 6 \][/tex]
3. Now, solve the absolute value equation by considering two cases:
- Case 1: When the expression inside the absolute value is positive:
[tex]\[ x + 7 = 6 \][/tex]
Subtract 7 from both sides:
[tex]\[ x = 6 - 7 \][/tex]
[tex]\[ x = -1 \][/tex]
- Case 2: When the expression inside the absolute value is negative:
[tex]\[ x + 7 = -6 \][/tex]
Subtract 7 from both sides:
[tex]\[ x = -6 - 7 \][/tex]
[tex]\[ x = -13 \][/tex]
So, the solutions to the equation are:
[tex]\[ x = -1 \][/tex]
and
[tex]\[ x = -13 \][/tex]
Therefore, the correct answer is:
B. [tex]\(x = -1\)[/tex] and [tex]\(x = -13\)[/tex]
Given the equation:
[tex]\[ 4|x+7| + 8 = 32 \][/tex]
1. First, isolate the absolute value term by subtracting 8 from both sides:
[tex]\[ 4|x+7| + 8 - 8 = 32 - 8 \][/tex]
[tex]\[ 4|x+7| = 24 \][/tex]
2. Next, divide both sides by 4 to further isolate the absolute value:
[tex]\[ \frac{4|x+7|}{4} = \frac{24}{4} \][/tex]
[tex]\[ |x+7| = 6 \][/tex]
3. Now, solve the absolute value equation by considering two cases:
- Case 1: When the expression inside the absolute value is positive:
[tex]\[ x + 7 = 6 \][/tex]
Subtract 7 from both sides:
[tex]\[ x = 6 - 7 \][/tex]
[tex]\[ x = -1 \][/tex]
- Case 2: When the expression inside the absolute value is negative:
[tex]\[ x + 7 = -6 \][/tex]
Subtract 7 from both sides:
[tex]\[ x = -6 - 7 \][/tex]
[tex]\[ x = -13 \][/tex]
So, the solutions to the equation are:
[tex]\[ x = -1 \][/tex]
and
[tex]\[ x = -13 \][/tex]
Therefore, the correct answer is:
B. [tex]\(x = -1\)[/tex] and [tex]\(x = -13\)[/tex]