Answer :
Sure! Let's solve the equation step-by-step:
We are given the equation:
[tex]\[ 4|x+7| + 8 = 32 \][/tex]
Step 1: Isolate the absolute value.
- Subtract 8 from both sides to simplify:
[tex]\[ 4|x+7| = 24 \][/tex]
Step 2: Divide both sides by 4 to solve for the absolute value.
- This gives us:
[tex]\[ |x+7| = 6 \][/tex]
Step 3: Solve the equation by considering the two scenarios for the absolute value.
- Case 1: When [tex]\( x + 7 = 6 \)[/tex]
- Solve for [tex]\( x \)[/tex] by subtracting 7 from both sides:
[tex]\[ x = 6 - 7 \][/tex]
[tex]\[ x = -1 \][/tex]
- Case 2: When [tex]\( x + 7 = -6 \)[/tex]
- Solve for [tex]\( x \)[/tex] by subtracting 7 from both sides:
[tex]\[ x = -6 - 7 \][/tex]
[tex]\[ x = -13 \][/tex]
Thus, the solutions for the equation [tex]\( 4|x+7| + 8 = 32 \)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -13 \)[/tex].
Therefore, the correct choice is B. [tex]\( x = -1 \)[/tex] and [tex]\( x = -13 \)[/tex].
We are given the equation:
[tex]\[ 4|x+7| + 8 = 32 \][/tex]
Step 1: Isolate the absolute value.
- Subtract 8 from both sides to simplify:
[tex]\[ 4|x+7| = 24 \][/tex]
Step 2: Divide both sides by 4 to solve for the absolute value.
- This gives us:
[tex]\[ |x+7| = 6 \][/tex]
Step 3: Solve the equation by considering the two scenarios for the absolute value.
- Case 1: When [tex]\( x + 7 = 6 \)[/tex]
- Solve for [tex]\( x \)[/tex] by subtracting 7 from both sides:
[tex]\[ x = 6 - 7 \][/tex]
[tex]\[ x = -1 \][/tex]
- Case 2: When [tex]\( x + 7 = -6 \)[/tex]
- Solve for [tex]\( x \)[/tex] by subtracting 7 from both sides:
[tex]\[ x = -6 - 7 \][/tex]
[tex]\[ x = -13 \][/tex]
Thus, the solutions for the equation [tex]\( 4|x+7| + 8 = 32 \)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -13 \)[/tex].
Therefore, the correct choice is B. [tex]\( x = -1 \)[/tex] and [tex]\( x = -13 \)[/tex].