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 :

Sure! Let's solve the equation [tex]\(|x + 5| - 6 = 7\)[/tex] step by step.

1. Isolate the absolute value term:

To isolate [tex]\(|x + 5|\)[/tex], add 6 to both sides of the equation:

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

This simplifies to:

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

2. Set up the two possible equations:

The absolute value equation [tex]\(|x + 5| = 13\)[/tex] means that [tex]\(x + 5\)[/tex] could be 13 or [tex]\(-13\)[/tex]. So, we set up two separate equations:

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

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

3. Solve each equation:

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

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

Subtract 5 from both sides:

[tex]\[
x = 13 - 5
\][/tex]

[tex]\[
x = 8
\][/tex]

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

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

Subtract 5 from both sides:

[tex]\[
x = -13 - 5
\][/tex]

[tex]\[
x = -18
\][/tex]

4. Write the solution:

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

So, the correct answer is:

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

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