Answer :
To solve the equation [tex]\( |x - 4| + 6 = 17 \)[/tex], we'll break it down into simple steps:
1. Isolate the Absolute Value Expression:
Start by isolating the absolute value by subtracting 6 from both sides:
[tex]\[
|x - 4| + 6 = 17 \\
|x - 4| = 17 - 6 \\
|x - 4| = 11
\][/tex]
2. Create Two Equations to Remove the Absolute Value:
The expression [tex]\( |x - 4| = 11 \)[/tex] implies two possible equations:
- Case 1: [tex]\( x - 4 = 11 \)[/tex]
- Case 2: [tex]\( x - 4 = -11 \)[/tex]
3. Solve Each Equation:
Case 1:
[tex]\[
x - 4 = 11
\][/tex]
Add 4 to both sides:
[tex]\[
x = 11 + 4 \\
x = 15
\][/tex]
Case 2:
[tex]\[
x - 4 = -11
\][/tex]
Add 4 to both sides:
[tex]\[
x = -11 + 4 \\
x = -7
\][/tex]
4. Combine the Solutions:
The solutions to the equation are [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex].
Thus, the correct choice is:
B. [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex]
1. Isolate the Absolute Value Expression:
Start by isolating the absolute value by subtracting 6 from both sides:
[tex]\[
|x - 4| + 6 = 17 \\
|x - 4| = 17 - 6 \\
|x - 4| = 11
\][/tex]
2. Create Two Equations to Remove the Absolute Value:
The expression [tex]\( |x - 4| = 11 \)[/tex] implies two possible equations:
- Case 1: [tex]\( x - 4 = 11 \)[/tex]
- Case 2: [tex]\( x - 4 = -11 \)[/tex]
3. Solve Each Equation:
Case 1:
[tex]\[
x - 4 = 11
\][/tex]
Add 4 to both sides:
[tex]\[
x = 11 + 4 \\
x = 15
\][/tex]
Case 2:
[tex]\[
x - 4 = -11
\][/tex]
Add 4 to both sides:
[tex]\[
x = -11 + 4 \\
x = -7
\][/tex]
4. Combine the Solutions:
The solutions to the equation are [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex].
Thus, the correct choice is:
B. [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex]
