Answer :
To solve the equation [tex]\(|x+5| - 6 = 7\)[/tex], we'll break it down step-by-step.
1. Isolate the Absolute Value:
Start by adding 6 to both sides of the equation to isolate the absolute value term.
[tex]\[
|x+5| - 6 + 6 = 7 + 6
\][/tex]
Simplifying, we have:
[tex]\[
|x+5| = 13
\][/tex]
2. Remove the Absolute Value:
The expression [tex]\(|x+5| = 13\)[/tex] means that the inside of the absolute value can be either equal to 13 or [tex]\(-13\)[/tex]. This gives us two separate equations to solve:
- First Equation:
[tex]\[
x + 5 = 13
\][/tex]
Solve for [tex]\(x\)[/tex] by subtracting 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- Second Equation:
[tex]\[
x + 5 = -13
\][/tex]
Solve for [tex]\(x\)[/tex] by subtracting 5 from both sides:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
3. Conclusion:
The solutions to the equation [tex]\(|x+5| - 6 = 7\)[/tex] are [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
Thus, the correct choice is A. [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 isolate the absolute value term.
[tex]\[
|x+5| - 6 + 6 = 7 + 6
\][/tex]
Simplifying, we have:
[tex]\[
|x+5| = 13
\][/tex]
2. Remove the Absolute Value:
The expression [tex]\(|x+5| = 13\)[/tex] means that the inside of the absolute value can be either equal to 13 or [tex]\(-13\)[/tex]. This gives us two separate equations to solve:
- First Equation:
[tex]\[
x + 5 = 13
\][/tex]
Solve for [tex]\(x\)[/tex] by subtracting 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- Second Equation:
[tex]\[
x + 5 = -13
\][/tex]
Solve for [tex]\(x\)[/tex] by subtracting 5 from both sides:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
3. Conclusion:
The solutions to the equation [tex]\(|x+5| - 6 = 7\)[/tex] are [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
Thus, the correct choice is A. [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].