Answer :
Let's solve the equation step by step:
The original equation is:
[tex]\[ 4|x+6| + 8 = 28 \][/tex]
1. Isolate the absolute value:
First, subtract 8 from both sides of the equation to help isolate the absolute value term:
[tex]\[ 4|x+6| = 20 \][/tex]
2. Divide both sides by 4:
[tex]\[ |x+6| = 5 \][/tex]
3. Consider the two cases for the absolute value:
An absolute value equation [tex]\(|x+6| = 5\)[/tex] can be split into two separate equations:
- Case 1: Positive scenario
[tex]\[ x + 6 = 5 \][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[ x = 5 - 6 \][/tex]
[tex]\[ x = -1 \][/tex]
- Case 2: Negative scenario
[tex]\[ x + 6 = -5 \][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[ x = -5 - 6 \][/tex]
[tex]\[ x = -11 \][/tex]
So, the solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex].
The correct answer is:
B. [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex]
The original equation is:
[tex]\[ 4|x+6| + 8 = 28 \][/tex]
1. Isolate the absolute value:
First, subtract 8 from both sides of the equation to help isolate the absolute value term:
[tex]\[ 4|x+6| = 20 \][/tex]
2. Divide both sides by 4:
[tex]\[ |x+6| = 5 \][/tex]
3. Consider the two cases for the absolute value:
An absolute value equation [tex]\(|x+6| = 5\)[/tex] can be split into two separate equations:
- Case 1: Positive scenario
[tex]\[ x + 6 = 5 \][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[ x = 5 - 6 \][/tex]
[tex]\[ x = -1 \][/tex]
- Case 2: Negative scenario
[tex]\[ x + 6 = -5 \][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[ x = -5 - 6 \][/tex]
[tex]\[ x = -11 \][/tex]
So, the solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex].
The correct answer is:
B. [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex]