Answer :
To solve the equation [tex]\(|x+5|-6=7\)[/tex], we need to handle the absolute value and isolate [tex]\(x\)[/tex]. Here's how you can do it step-by-step:
1. Isolate the absolute value: Start by adding 6 to both sides of the equation to get rid of the [tex]\(-6\)[/tex] on the left side.
[tex]\[
|x+5| = 7 + 6
\][/tex]
[tex]\[
|x+5| = 13
\][/tex]
2. Remove the absolute value: An absolute value equation like [tex]\(|x+5| = 13\)[/tex] can have two possible solutions, because the expression inside the absolute value can be both 13 and -13:
- First possibility: [tex]\(x + 5 = 13\)[/tex]
- Second possibility: [tex]\(x + 5 = -13\)[/tex]
3. Solve each equation:
- For the first equation, [tex]\(x + 5 = 13\)[/tex]:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For the second equation, [tex]\(x + 5 = -13\)[/tex]:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
Therefore, the solutions are [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex]. So, the correct answer is [tex]\(D. \, x=8 \text{ and } x=-18\)[/tex].
1. Isolate the absolute value: Start by adding 6 to both sides of the equation to get rid of the [tex]\(-6\)[/tex] on the left side.
[tex]\[
|x+5| = 7 + 6
\][/tex]
[tex]\[
|x+5| = 13
\][/tex]
2. Remove the absolute value: An absolute value equation like [tex]\(|x+5| = 13\)[/tex] can have two possible solutions, because the expression inside the absolute value can be both 13 and -13:
- First possibility: [tex]\(x + 5 = 13\)[/tex]
- Second possibility: [tex]\(x + 5 = -13\)[/tex]
3. Solve each equation:
- For the first equation, [tex]\(x + 5 = 13\)[/tex]:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For the second equation, [tex]\(x + 5 = -13\)[/tex]:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
Therefore, the solutions are [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex]. So, the correct answer is [tex]\(D. \, x=8 \text{ and } x=-18\)[/tex].