Answer :
Sure, let's solve the equation [tex]\( |x+5|-6=7 \)[/tex] step by step.
1. Isolate the absolute value:
Start by adding 6 to both sides of the equation to remove the constant term outside the absolute value:
[tex]\[
|x+5| - 6 + 6 = 7 + 6
\][/tex]
[tex]\[
|x+5| = 13
\][/tex]
2. Set up the two cases for the absolute value:
The absolute value expression [tex]\( |x+5| = 13 \)[/tex] means that the expression inside the absolute value, [tex]\( x+5 \)[/tex], can be either 13 or -13.
Case 1: [tex]\( x+5 = 13 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x+5 = 13
\][/tex]
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
Case 2: [tex]\( x+5 = -13 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x+5 = -13
\][/tex]
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
3. Write the solution:
The solutions to the equation are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex]
1. Isolate the absolute value:
Start by adding 6 to both sides of the equation to remove the constant term outside the absolute value:
[tex]\[
|x+5| - 6 + 6 = 7 + 6
\][/tex]
[tex]\[
|x+5| = 13
\][/tex]
2. Set up the two cases for the absolute value:
The absolute value expression [tex]\( |x+5| = 13 \)[/tex] means that the expression inside the absolute value, [tex]\( x+5 \)[/tex], can be either 13 or -13.
Case 1: [tex]\( x+5 = 13 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x+5 = 13
\][/tex]
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
Case 2: [tex]\( x+5 = -13 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x+5 = -13
\][/tex]
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
3. Write the solution:
The solutions to the equation are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex]