Answer :
To solve the equation [tex]\( |x + 5| - 6 = 7 \)[/tex], follow these steps:
1. Isolate the Absolute Value:
Start by adding 6 to both sides of the equation to isolate the absolute value expression:
[tex]\[
|x + 5| - 6 + 6 = 7 + 6
\][/tex]
[tex]\[
|x + 5| = 13
\][/tex]
2. Set Up Two Cases:
The equation [tex]\( |x + 5| = 13 \)[/tex] indicates two possible scenarios because absolute value measures the distance from zero:
- Positive Case: [tex]\( x + 5 = 13 \)[/tex]
- Negative Case: [tex]\( x + 5 = -13 \)[/tex]
3. Solve Each Case:
- For the Positive Case:
[tex]\[
x + 5 = 13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For the Negative Case:
[tex]\[
x + 5 = -13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
4. Conclusion:
The solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Given the options provided, 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 isolate the absolute value expression:
[tex]\[
|x + 5| - 6 + 6 = 7 + 6
\][/tex]
[tex]\[
|x + 5| = 13
\][/tex]
2. Set Up Two Cases:
The equation [tex]\( |x + 5| = 13 \)[/tex] indicates two possible scenarios because absolute value measures the distance from zero:
- Positive Case: [tex]\( x + 5 = 13 \)[/tex]
- Negative Case: [tex]\( x + 5 = -13 \)[/tex]
3. Solve Each Case:
- For the Positive Case:
[tex]\[
x + 5 = 13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For the Negative Case:
[tex]\[
x + 5 = -13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
4. Conclusion:
The solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Given the options provided, the correct answer is:
C. [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex]