High School

Solve [tex]|x+5|-6=7[/tex]

A. [tex]x=8[/tex] and [tex]x=-18[/tex]

B. [tex]x=-8[/tex] and [tex]x=-18[/tex]

C. [tex]x=-8[/tex] and [tex]x=18[/tex]

D. [tex]x=8[/tex] and [tex]x=-8[/tex]

Answer :

To solve the equation [tex]\( |x+5| - 6 = 7 \)[/tex], let's break it down step by step:

1. Isolate the Absolute Value:
Start by getting rid of the [tex]\(-6\)[/tex] on the left side of the equation by adding [tex]\(6\)[/tex] to both sides:
[tex]\[
|x+5| - 6 + 6 = 7 + 6
\][/tex]
[tex]\[
|x+5| = 13
\][/tex]

2. Understand the Absolute Value:
The equation [tex]\( |x+5| = 13 \)[/tex] means that the expression inside the absolute value, [tex]\( x+5 \)[/tex], can be either equal to [tex]\(13\)[/tex] or [tex]\(-13\)[/tex] because absolute value signifies the distance from zero, which can be in either direction on the number line.

3. Set up Two Separate Equations:
- Equation 1: [tex]\( x+5 = 13 \)[/tex]
- Equation 2: [tex]\( x+5 = -13 \)[/tex]

4. Solve Each Equation:
- For Equation 1 [tex]\( x+5 = 13 \)[/tex]:
Subtract [tex]\(5\)[/tex] from both sides:
[tex]\[
x+5-5 = 13-5
\][/tex]
[tex]\[
x = 8
\][/tex]

- For Equation 2 [tex]\( x+5 = -13 \)[/tex]:
Subtract [tex]\(5\)[/tex] from both sides:
[tex]\[
x+5-5 = -13-5
\][/tex]
[tex]\[
x = -18
\][/tex]

5. Conclusion:
The solutions to the equation [tex]\( |x+5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].

Thus, the correct answer is A. [tex]\(x=8\)[/tex] and [tex]\(x=-18\)[/tex].