Answer :
Sure, let's solve the absolute value equation step-by-step:
The given equation is:
[tex]\[ |2(x - 5)| + 11 = 17 \][/tex]
First, let's isolate the absolute value expression by subtracting 11 from both sides:
[tex]\[ |2(x - 5)| = 17 - 11 \][/tex]
[tex]\[ |2(x - 5)| = 6 \][/tex]
An absolute value equation [tex]\(|A| = B\)[/tex] means that [tex]\(A\)[/tex] can either be [tex]\(B\)[/tex] or [tex]\(-B\)[/tex]. Therefore, we have two cases to consider:
Case 1:
[tex]\[ 2(x - 5) = 6 \][/tex]
- Solve for [tex]\(x\)[/tex]:
[tex]\[ 2(x - 5) = 6 \][/tex]
Divide both sides by 2:
[tex]\[ x - 5 = 3 \][/tex]
Add 5 to both sides:
[tex]\[ x = 8 \][/tex]
Case 2:
[tex]\[ 2(x - 5) = -6 \][/tex]
- Solve for [tex]\(x\)[/tex]:
[tex]\[ 2(x - 5) = -6 \][/tex]
Divide both sides by 2:
[tex]\[ x - 5 = -3 \][/tex]
Add 5 to both sides:
[tex]\[ x = 2 \][/tex]
So, the solutions to the equation are [tex]\(x = 8\)[/tex] and [tex]\(x = 2\)[/tex].
The correct answer choice is:
(C) [tex]\(x = 8\)[/tex] and [tex]\(x = 2\)[/tex]
The given equation is:
[tex]\[ |2(x - 5)| + 11 = 17 \][/tex]
First, let's isolate the absolute value expression by subtracting 11 from both sides:
[tex]\[ |2(x - 5)| = 17 - 11 \][/tex]
[tex]\[ |2(x - 5)| = 6 \][/tex]
An absolute value equation [tex]\(|A| = B\)[/tex] means that [tex]\(A\)[/tex] can either be [tex]\(B\)[/tex] or [tex]\(-B\)[/tex]. Therefore, we have two cases to consider:
Case 1:
[tex]\[ 2(x - 5) = 6 \][/tex]
- Solve for [tex]\(x\)[/tex]:
[tex]\[ 2(x - 5) = 6 \][/tex]
Divide both sides by 2:
[tex]\[ x - 5 = 3 \][/tex]
Add 5 to both sides:
[tex]\[ x = 8 \][/tex]
Case 2:
[tex]\[ 2(x - 5) = -6 \][/tex]
- Solve for [tex]\(x\)[/tex]:
[tex]\[ 2(x - 5) = -6 \][/tex]
Divide both sides by 2:
[tex]\[ x - 5 = -3 \][/tex]
Add 5 to both sides:
[tex]\[ x = 2 \][/tex]
So, the solutions to the equation are [tex]\(x = 8\)[/tex] and [tex]\(x = 2\)[/tex].
The correct answer choice is:
(C) [tex]\(x = 8\)[/tex] and [tex]\(x = 2\)[/tex]