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 :

Certainly! Let's solve the equation step by step:

The equation is [tex]\( |x+5| - 6 = 7 \)[/tex].

1. Isolate the absolute value:

Add 6 to both sides to isolate the absolute value:

[tex]\[
|x+5| = 13
\][/tex]

2. Consider the two cases for the absolute value:

When you have an equation involving absolute value [tex]\( |A| = B \)[/tex], it means:

[tex]\( A = B \)[/tex] or [tex]\( A = -B \)[/tex].

So here, we have:

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

3. Solve each case:

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

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

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

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

4. Conclusion:

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

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