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], we need to follow these steps:

1. Isolate the absolute value:
[tex]\[
|x + 5| - 6 = 7
\][/tex]
Add 6 to both sides:
[tex]\[
|x + 5| = 13
\][/tex]

2. Consider the definition of absolute value:

The equation [tex]\( |x + 5| = 13 \)[/tex] means that [tex]\( x + 5 \)[/tex] can be either 13 or -13.

3. Set up the two possible equations:

Case 1: [tex]\( x + 5 = 13 \)[/tex]
Case 2: [tex]\( x + 5 = -13 \)[/tex]

4. Solve each equation:

For Case 1:
[tex]\[
x + 5 = 13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]

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

So, the solutions to the equation are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].

Therefore, the correct answer is:

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

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