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

Answer :

To solve the equation [tex]\(|x + 5| - 6 = 7\)[/tex], we'll go through it step by step.

1. Isolate the absolute value:

Start by adding 6 to both sides of the equation:
[tex]\[
|x + 5| = 13
\][/tex]

2. Set up two separate equations:

Since the absolute value of a number can be either positive or negative, we need to consider two cases:

a) [tex]\(x + 5 = 13\)[/tex]

b) [tex]\(x + 5 = -13\)[/tex]

3. Solve each equation:

- For [tex]\(x + 5 = 13\)[/tex]:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]

- For [tex]\(x + 5 = -13\)[/tex]:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]

4. Check the solutions:

It's always a good idea to verify the solutions by substituting them back into the original equation to ensure they satisfy it.

- For [tex]\(x = 8\)[/tex]:
[tex]\[
|8 + 5| - 6 = |13| - 6 = 13 - 6 = 7
\][/tex]
This is true.

- For [tex]\(x = -18\)[/tex]:
[tex]\[
|-18 + 5| - 6 = |-13| - 6 = 13 - 6 = 7
\][/tex]
This is also true.

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

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

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