Answer :
Sure, let's solve the equation [tex]\(4|x+6| + 8 = 28\)[/tex] step-by-step:
1. Isolate the Absolute Value Expression:
Start by subtracting 8 from both sides of the equation:
[tex]\[
4|x+6| + 8 - 8 = 28 - 8
\][/tex]
[tex]\[
4|x+6| = 20
\][/tex]
2. Solve for the Absolute Value Term:
Divide both sides by 4 to isolate the absolute value:
[tex]\[
|x+6| = \frac{20}{4}
\][/tex]
[tex]\[
|x+6| = 5
\][/tex]
3. Set Up Two Separate Equations:
The expression [tex]\(|x+6| = 5\)[/tex] means that [tex]\(x+6\)[/tex] can be either 5 or -5. So we set up two equations:
- [tex]\(x+6 = 5\)[/tex]
- [tex]\(x+6 = -5\)[/tex]
4. Solve Each Equation:
- For [tex]\(x+6 = 5\)[/tex]:
[tex]\[
x = 5 - 6
\][/tex]
[tex]\[
x = -1
\][/tex]
- For [tex]\(x+6 = -5\)[/tex]:
[tex]\[
x = -5 - 6
\][/tex]
[tex]\[
x = -11
\][/tex]
5. Conclusion:
The solutions to the equation [tex]\(4|x+6|+8=28\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex].
Therefore, the correct answer is A. [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex].
1. Isolate the Absolute Value Expression:
Start by subtracting 8 from both sides of the equation:
[tex]\[
4|x+6| + 8 - 8 = 28 - 8
\][/tex]
[tex]\[
4|x+6| = 20
\][/tex]
2. Solve for the Absolute Value Term:
Divide both sides by 4 to isolate the absolute value:
[tex]\[
|x+6| = \frac{20}{4}
\][/tex]
[tex]\[
|x+6| = 5
\][/tex]
3. Set Up Two Separate Equations:
The expression [tex]\(|x+6| = 5\)[/tex] means that [tex]\(x+6\)[/tex] can be either 5 or -5. So we set up two equations:
- [tex]\(x+6 = 5\)[/tex]
- [tex]\(x+6 = -5\)[/tex]
4. Solve Each Equation:
- For [tex]\(x+6 = 5\)[/tex]:
[tex]\[
x = 5 - 6
\][/tex]
[tex]\[
x = -1
\][/tex]
- For [tex]\(x+6 = -5\)[/tex]:
[tex]\[
x = -5 - 6
\][/tex]
[tex]\[
x = -11
\][/tex]
5. Conclusion:
The solutions to the equation [tex]\(4|x+6|+8=28\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex].
Therefore, the correct answer is A. [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex].