Answer :
To solve the equation [tex]\(4|x+6|+8=28\)[/tex], follow these steps:
1. Isolate the Absolute Value:
Start by isolating the absolute value expression on one side of the equation:
[tex]\[
4|x+6| + 8 = 28
\][/tex]
Subtract 8 from both sides to get:
[tex]\[
4|x+6| = 20
\][/tex]
2. Divide to Simplify:
Divide both sides by 4 to simplify:
[tex]\[
|x+6| = 5
\][/tex]
3. Consider the Two Scenarios:
The equation [tex]\(|x+6| = 5\)[/tex] means that what’s inside the absolute value can either be 5 or -5. This gives us two separate equations to solve:
- Case 1: [tex]\(x+6 = 5\)[/tex]
- Subtract 6 from both sides:
[tex]\[
x = 5 - 6 = -1
\][/tex]
- Case 2: [tex]\(x+6 = -5\)[/tex]
- Subtract 6 from both sides:
[tex]\[
x = -5 - 6 = -11
\][/tex]
4. Solution:
The solutions are [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex].
So, the correct answer is D. [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex].
1. Isolate the Absolute Value:
Start by isolating the absolute value expression on one side of the equation:
[tex]\[
4|x+6| + 8 = 28
\][/tex]
Subtract 8 from both sides to get:
[tex]\[
4|x+6| = 20
\][/tex]
2. Divide to Simplify:
Divide both sides by 4 to simplify:
[tex]\[
|x+6| = 5
\][/tex]
3. Consider the Two Scenarios:
The equation [tex]\(|x+6| = 5\)[/tex] means that what’s inside the absolute value can either be 5 or -5. This gives us two separate equations to solve:
- Case 1: [tex]\(x+6 = 5\)[/tex]
- Subtract 6 from both sides:
[tex]\[
x = 5 - 6 = -1
\][/tex]
- Case 2: [tex]\(x+6 = -5\)[/tex]
- Subtract 6 from both sides:
[tex]\[
x = -5 - 6 = -11
\][/tex]
4. Solution:
The solutions are [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex].
So, the correct answer is D. [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex].