Answer :
To solve the equation [tex]\( |x-5| + 7 = 17 \)[/tex], we can follow these steps:
1. Isolate the Absolute Value: Start by subtracting 7 from both sides of the equation to get:
[tex]\[
|x-5| = 10
\][/tex]
2. Set Up Two Cases: Since the absolute value of a number is the distance from zero, it results in two possible equations:
- [tex]\( x - 5 = 10 \)[/tex]
- [tex]\( x - 5 = -10 \)[/tex]
3. Solve Each Equation:
- For [tex]\( x - 5 = 10 \)[/tex]:
[tex]\[
x = 10 + 5 = 15
\][/tex]
- For [tex]\( x - 5 = -10 \)[/tex]:
[tex]\[
x = -10 + 5 = -5
\][/tex]
4. List the Solutions: The solutions to the equation are [tex]\( x = 15 \)[/tex] and [tex]\( x = -5 \)[/tex].
Thus, the correct answer is:
D. [tex]\( x = 15 \)[/tex] and [tex]\( x = -5 \)[/tex].
1. Isolate the Absolute Value: Start by subtracting 7 from both sides of the equation to get:
[tex]\[
|x-5| = 10
\][/tex]
2. Set Up Two Cases: Since the absolute value of a number is the distance from zero, it results in two possible equations:
- [tex]\( x - 5 = 10 \)[/tex]
- [tex]\( x - 5 = -10 \)[/tex]
3. Solve Each Equation:
- For [tex]\( x - 5 = 10 \)[/tex]:
[tex]\[
x = 10 + 5 = 15
\][/tex]
- For [tex]\( x - 5 = -10 \)[/tex]:
[tex]\[
x = -10 + 5 = -5
\][/tex]
4. List the Solutions: The solutions to the equation are [tex]\( x = 15 \)[/tex] and [tex]\( x = -5 \)[/tex].
Thus, the correct answer is:
D. [tex]\( x = 15 \)[/tex] and [tex]\( x = -5 \)[/tex].
