Answer :
To solve the equation [tex]\( |x+5|-6=7 \)[/tex], follow these steps:
1. Isolate the absolute value expression:
Begin by adding 6 to both sides of the equation to get rid of the [tex]\(-6\)[/tex] term:
[tex]\[
|x+5| - 6 + 6 = 7 + 6
\][/tex]
This simplifies to:
[tex]\[
|x+5| = 13
\][/tex]
2. Understand what the absolute value means:
The equation [tex]\( |x+5| = 13 \)[/tex] means that the expression inside the absolute value, [tex]\( x+5 \)[/tex], can be either 13 or -13 because the absolute value of a number is the distance from zero and can be positive or negative:
[tex]\[
x+5 = 13 \quad \text{or} \quad x+5 = -13
\][/tex]
3. Solve both equations:
- Case 1: Solve [tex]\( x+5 = 13 \)[/tex]
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- Case 2: Solve [tex]\( x+5 = -13 \)[/tex]
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
So, the solutions to the equation [tex]\( |x+5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex]. These correspond to option B: [tex]\( x=8 \)[/tex] and [tex]\( x=-18 \)[/tex].
1. Isolate the absolute value expression:
Begin by adding 6 to both sides of the equation to get rid of the [tex]\(-6\)[/tex] term:
[tex]\[
|x+5| - 6 + 6 = 7 + 6
\][/tex]
This simplifies to:
[tex]\[
|x+5| = 13
\][/tex]
2. Understand what the absolute value means:
The equation [tex]\( |x+5| = 13 \)[/tex] means that the expression inside the absolute value, [tex]\( x+5 \)[/tex], can be either 13 or -13 because the absolute value of a number is the distance from zero and can be positive or negative:
[tex]\[
x+5 = 13 \quad \text{or} \quad x+5 = -13
\][/tex]
3. Solve both equations:
- Case 1: Solve [tex]\( x+5 = 13 \)[/tex]
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- Case 2: Solve [tex]\( x+5 = -13 \)[/tex]
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
So, the solutions to the equation [tex]\( |x+5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex]. These correspond to option B: [tex]\( x=8 \)[/tex] and [tex]\( x=-18 \)[/tex].