Answer :
To solve the equation [tex]\(|x-4| + 6 = 17\)[/tex], we need to isolate the absolute value expression. Here’s how you do it step-by-step:
1. Isolate the Absolute Value: Start by getting rid of the extra constant outside the absolute value. We do this by subtracting 6 from both sides of the equation:
[tex]\[
|x-4| + 6 - 6 = 17 - 6
\][/tex]
This simplifies to:
[tex]\[
|x-4| = 11
\][/tex]
2. Remove the Absolute Value: The equation [tex]\(|x-4| = 11\)[/tex] means that the expression inside the absolute value can be either 11 or -11. So, set up two separate equations:
- Equation 1: [tex]\(x - 4 = 11\)[/tex]
- Equation 2: [tex]\(x - 4 = -11\)[/tex]
3. Solve Each Equation:
- For the first equation, [tex]\(x - 4 = 11\)[/tex]:
[tex]\[
x = 11 + 4
\][/tex]
[tex]\[
x = 15
\][/tex]
- For the second equation, [tex]\(x - 4 = -11\)[/tex]:
[tex]\[
x = -11 + 4
\][/tex]
[tex]\[
x = -7
\][/tex]
4. Write the Solutions: The solutions to the original equation are [tex]\(x = 15\)[/tex] and [tex]\(x = -7\)[/tex].
So, the correct answer is B. [tex]\(x = 15\)[/tex] and [tex]\(x = -7\)[/tex].
1. Isolate the Absolute Value: Start by getting rid of the extra constant outside the absolute value. We do this by subtracting 6 from both sides of the equation:
[tex]\[
|x-4| + 6 - 6 = 17 - 6
\][/tex]
This simplifies to:
[tex]\[
|x-4| = 11
\][/tex]
2. Remove the Absolute Value: The equation [tex]\(|x-4| = 11\)[/tex] means that the expression inside the absolute value can be either 11 or -11. So, set up two separate equations:
- Equation 1: [tex]\(x - 4 = 11\)[/tex]
- Equation 2: [tex]\(x - 4 = -11\)[/tex]
3. Solve Each Equation:
- For the first equation, [tex]\(x - 4 = 11\)[/tex]:
[tex]\[
x = 11 + 4
\][/tex]
[tex]\[
x = 15
\][/tex]
- For the second equation, [tex]\(x - 4 = -11\)[/tex]:
[tex]\[
x = -11 + 4
\][/tex]
[tex]\[
x = -7
\][/tex]
4. Write the Solutions: The solutions to the original equation are [tex]\(x = 15\)[/tex] and [tex]\(x = -7\)[/tex].
So, the correct answer is B. [tex]\(x = 15\)[/tex] and [tex]\(x = -7\)[/tex].
