Answer :
Sure, let's solve the equation step-by-step:
We start with the equation:
[tex]\[ 4|x + 7| + 8 = 32 \][/tex]
Step 1: First, let's isolate the absolute value expression by subtracting 8 from both sides:
[tex]\[ 4|x + 7| = 24 \][/tex]
Step 2: Next, divide both sides by 4 to solve for the absolute value:
[tex]\[ |x + 7| = 6 \][/tex]
Step 3: The absolute value equation [tex]\(|x + 7| = 6\)[/tex] means there are two possible cases:
- Case 1: [tex]\(x + 7 = 6\)[/tex]
- Case 2: [tex]\(x + 7 = -6\)[/tex]
Let's solve each case:
Case 1:
[tex]\[ x + 7 = 6 \][/tex]
Subtract 7 from both sides:
[tex]\[ x = 6 - 7 \][/tex]
[tex]\[ x = -1 \][/tex]
Case 2:
[tex]\[ x + 7 = -6 \][/tex]
Subtract 7 from both sides:
[tex]\[ x = -6 - 7 \][/tex]
[tex]\[ x = -13 \][/tex]
So the solutions for the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -13\)[/tex].
However, it seems there's a mistake in the provided answer options. From our work, the correct solutions should be [tex]\(x = -1\)[/tex] and [tex]\(x = -13\)[/tex]. None of the given options [tex]\(A\)[/tex], [tex]\(B\)[/tex], [tex]\(C\)[/tex], or [tex]\(D\)[/tex] match this. If there are more options or a typo, kindly review them.
We start with the equation:
[tex]\[ 4|x + 7| + 8 = 32 \][/tex]
Step 1: First, let's isolate the absolute value expression by subtracting 8 from both sides:
[tex]\[ 4|x + 7| = 24 \][/tex]
Step 2: Next, divide both sides by 4 to solve for the absolute value:
[tex]\[ |x + 7| = 6 \][/tex]
Step 3: The absolute value equation [tex]\(|x + 7| = 6\)[/tex] means there are two possible cases:
- Case 1: [tex]\(x + 7 = 6\)[/tex]
- Case 2: [tex]\(x + 7 = -6\)[/tex]
Let's solve each case:
Case 1:
[tex]\[ x + 7 = 6 \][/tex]
Subtract 7 from both sides:
[tex]\[ x = 6 - 7 \][/tex]
[tex]\[ x = -1 \][/tex]
Case 2:
[tex]\[ x + 7 = -6 \][/tex]
Subtract 7 from both sides:
[tex]\[ x = -6 - 7 \][/tex]
[tex]\[ x = -13 \][/tex]
So the solutions for the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -13\)[/tex].
However, it seems there's a mistake in the provided answer options. From our work, the correct solutions should be [tex]\(x = -1\)[/tex] and [tex]\(x = -13\)[/tex]. None of the given options [tex]\(A\)[/tex], [tex]\(B\)[/tex], [tex]\(C\)[/tex], or [tex]\(D\)[/tex] match this. If there are more options or a typo, kindly review them.