Answer :
To solve the equation [tex]\( |x + 5| - 6 = 7 \)[/tex], we'll follow these steps:
1. Isolate the Absolute Value:
Start by moving the -6 to the other side of the equation:
[tex]\[
|x + 5| = 7 + 6
\][/tex]
Simplify the right side to get:
[tex]\[
|x + 5| = 13
\][/tex]
2. Consider the Definition of Absolute Value:
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. This gives us two separate equations:
- [tex]\( x + 5 = 13 \)[/tex]
- [tex]\( x + 5 = -13 \)[/tex]
3. Solve Each Equation:
- For [tex]\( x + 5 = 13 \)[/tex]:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For [tex]\( x + 5 = -13 \)[/tex]:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
4. Solutions:
The solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Therefore, the correct answer is option D: [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
1. Isolate the Absolute Value:
Start by moving the -6 to the other side of the equation:
[tex]\[
|x + 5| = 7 + 6
\][/tex]
Simplify the right side to get:
[tex]\[
|x + 5| = 13
\][/tex]
2. Consider the Definition of Absolute Value:
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. This gives us two separate equations:
- [tex]\( x + 5 = 13 \)[/tex]
- [tex]\( x + 5 = -13 \)[/tex]
3. Solve Each Equation:
- For [tex]\( x + 5 = 13 \)[/tex]:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For [tex]\( x + 5 = -13 \)[/tex]:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
4. Solutions:
The solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Therefore, the correct answer is option D: [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].