College

Solve [tex]|x-5|+7=17[/tex]

A. [tex]x=-15[/tex] and [tex]x=5[/tex]
B. [tex]x=-15[/tex] and [tex]x=-5[/tex]
C. [tex]x=15[/tex] and [tex]x=-15[/tex]
D. [tex]x=15[/tex] and [tex]x=-5[/tex]

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].