Answer :
To solve the equation [tex]\( |x-5| + 7 = 17 \)[/tex], we need to first isolate the absolute value expression. Here’s how we can do it step-by-step:
1. Isolate the Absolute Value:
Start by subtracting 7 from both sides of the equation:
[tex]\[
|x-5| + 7 - 7 = 17 - 7
\][/tex]
This simplifies to:
[tex]\[
|x-5| = 10
\][/tex]
2. Remove the Absolute Value:
The equation [tex]\( |x-5| = 10 \)[/tex] tells us that the expression inside the absolute value, [tex]\( x-5 \)[/tex], can be either 10 or -10. This leads us to two separate equations:
- [tex]\( x - 5 = 10 \)[/tex]
- [tex]\( x - 5 = -10 \)[/tex]
3. Solve Each Equation:
- For the first equation [tex]\( x - 5 = 10 \)[/tex]:
[tex]\[
x = 10 + 5 = 15
\][/tex]
- For the second equation [tex]\( x - 5 = -10 \)[/tex]:
[tex]\[
x = -10 + 5 = -5
\][/tex]
4. Solutions:
The values of [tex]\( x \)[/tex] that satisfy the original equation are [tex]\( x = 15 \)[/tex] and [tex]\( x = -5 \)[/tex].
Therefore, the correct answer is:
A. [tex]\( x = 15 \)[/tex] and [tex]\( x = -5 \)[/tex].
1. Isolate the Absolute Value:
Start by subtracting 7 from both sides of the equation:
[tex]\[
|x-5| + 7 - 7 = 17 - 7
\][/tex]
This simplifies to:
[tex]\[
|x-5| = 10
\][/tex]
2. Remove the Absolute Value:
The equation [tex]\( |x-5| = 10 \)[/tex] tells us that the expression inside the absolute value, [tex]\( x-5 \)[/tex], can be either 10 or -10. This leads us to two separate equations:
- [tex]\( x - 5 = 10 \)[/tex]
- [tex]\( x - 5 = -10 \)[/tex]
3. Solve Each Equation:
- For the first equation [tex]\( x - 5 = 10 \)[/tex]:
[tex]\[
x = 10 + 5 = 15
\][/tex]
- For the second equation [tex]\( x - 5 = -10 \)[/tex]:
[tex]\[
x = -10 + 5 = -5
\][/tex]
4. Solutions:
The values of [tex]\( x \)[/tex] that satisfy the original equation are [tex]\( x = 15 \)[/tex] and [tex]\( x = -5 \)[/tex].
Therefore, the correct answer is:
A. [tex]\( x = 15 \)[/tex] and [tex]\( x = -5 \)[/tex].
