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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 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].

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