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Answer :
To solve the equation [tex]\( |x-1| + 6 = 17 \)[/tex], follow these steps:
1. Isolate the absolute value:
- Start by subtracting 6 from both sides of the equation to isolate the absolute value term:
[tex]\[
|x-1| + 6 - 6 = 17 - 6
\][/tex]
[tex]\[
|x-1| = 11
\][/tex]
2. Remove the absolute value:
- The equation [tex]\( |x-1| = 11 \)[/tex] means that the expression inside the absolute value can either be 11 or -11. This gives us two separate equations to solve:
- Equation 1: [tex]\( x-1 = 11 \)[/tex]
- Equation 2: [tex]\( x-1 = -11 \)[/tex]
3. Solve each equation:
- Equation 1: [tex]\( x-1 = 11 \)[/tex]
- Add 1 to both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x - 1 + 1 = 11 + 1
\][/tex]
[tex]\[
x = 12
\][/tex]
- Equation 2: [tex]\( x-1 = -11 \)[/tex]
- Add 1 to both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x - 1 + 1 = -11 + 1
\][/tex]
[tex]\[
x = -10
\][/tex]
4. Solutions:
- The solutions to the equation [tex]\( |x-1| + 6 = 17 \)[/tex] are [tex]\( x = 12 \)[/tex] and [tex]\( x = -10 \)[/tex].
Thus, there aren't any options matching the calculated values exactly, suggesting the given options may be incorrect in this case. If you're solving problems like this on a test or assignment, always verify your work and ensure the calculations align with the given choices.
1. Isolate the absolute value:
- Start by subtracting 6 from both sides of the equation to isolate the absolute value term:
[tex]\[
|x-1| + 6 - 6 = 17 - 6
\][/tex]
[tex]\[
|x-1| = 11
\][/tex]
2. Remove the absolute value:
- The equation [tex]\( |x-1| = 11 \)[/tex] means that the expression inside the absolute value can either be 11 or -11. This gives us two separate equations to solve:
- Equation 1: [tex]\( x-1 = 11 \)[/tex]
- Equation 2: [tex]\( x-1 = -11 \)[/tex]
3. Solve each equation:
- Equation 1: [tex]\( x-1 = 11 \)[/tex]
- Add 1 to both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x - 1 + 1 = 11 + 1
\][/tex]
[tex]\[
x = 12
\][/tex]
- Equation 2: [tex]\( x-1 = -11 \)[/tex]
- Add 1 to both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x - 1 + 1 = -11 + 1
\][/tex]
[tex]\[
x = -10
\][/tex]
4. Solutions:
- The solutions to the equation [tex]\( |x-1| + 6 = 17 \)[/tex] are [tex]\( x = 12 \)[/tex] and [tex]\( x = -10 \)[/tex].
Thus, there aren't any options matching the calculated values exactly, suggesting the given options may be incorrect in this case. If you're solving problems like this on a test or assignment, always verify your work and ensure the calculations align with the given choices.
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