Answer :
Sure, let's solve the equation [tex]\( |x - 4| + 6 = 17 \)[/tex] step-by-step.
1. Isolate the absolute value expression:
[tex]\[
|x - 4| + 6 = 17
\][/tex]
Subtract 6 from both sides:
[tex]\[
|x - 4| = 11
\][/tex]
2. Consider the definition of absolute value:
The equation [tex]\( |x - 4| = 11 \)[/tex] means that [tex]\( x - 4 \)[/tex] can be either 11 or -11.
3. Set up the two possible cases:
- Case 1: [tex]\( x - 4 = 11 \)[/tex]
- Case 2: [tex]\( x - 4 = -11 \)[/tex]
4. Solve each case:
- For Case 1:
[tex]\[
x - 4 = 11
\][/tex]
Add 4 to both sides:
[tex]\[
x = 15
\][/tex]
- For Case 2:
[tex]\[
x - 4 = -11
\][/tex]
Add 4 to both sides:
[tex]\[
x = -7
\][/tex]
5. Combine the results:
The solutions to the equation are [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex].
So, the correct answer is:
A. [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex]
1. Isolate the absolute value expression:
[tex]\[
|x - 4| + 6 = 17
\][/tex]
Subtract 6 from both sides:
[tex]\[
|x - 4| = 11
\][/tex]
2. Consider the definition of absolute value:
The equation [tex]\( |x - 4| = 11 \)[/tex] means that [tex]\( x - 4 \)[/tex] can be either 11 or -11.
3. Set up the two possible cases:
- Case 1: [tex]\( x - 4 = 11 \)[/tex]
- Case 2: [tex]\( x - 4 = -11 \)[/tex]
4. Solve each case:
- For Case 1:
[tex]\[
x - 4 = 11
\][/tex]
Add 4 to both sides:
[tex]\[
x = 15
\][/tex]
- For Case 2:
[tex]\[
x - 4 = -11
\][/tex]
Add 4 to both sides:
[tex]\[
x = -7
\][/tex]
5. Combine the results:
The solutions to the equation are [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex].
So, the correct answer is:
A. [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex]
