College

Solve [tex]$4|x+6|+8=28$[/tex].

A. [tex]$x=1$[/tex] and [tex][tex]$x=-1$[/tex][/tex]

B. [tex]$x=1$[/tex] and [tex]$x=-11$[/tex]

C. [tex][tex]$x=-1$[/tex][/tex] and [tex]$x=11$[/tex]

D. [tex]$x=-1$[/tex] and [tex][tex]$x=-11$[/tex][/tex]

Answer :

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]

Simplifying this, we get:

[tex]\[
4|x+6| = 20
\][/tex]

2. Divide to Simplify:

Divide both sides by 4 to solve for the absolute value:

[tex]\[
|x+6| = \frac{20}{4}
\][/tex]

This gives:

[tex]\[
|x+6| = 5
\][/tex]

3. Set Up Two Scenarios:

Since [tex]\(|x+6| = 5\)[/tex], there are two possible scenarios:

- [tex]\(x + 6 = 5\)[/tex]
- [tex]\(x + 6 = -5\)[/tex]

4. Solve Each Scenario:

Scenario 1:
Solve [tex]\(x + 6 = 5\)[/tex]:

[tex]\[
x = 5 - 6
\][/tex]

[tex]\[
x = -1
\][/tex]

Scenario 2:
Solve [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:

D. [tex]\(x = -1\)[/tex] and [tex]\(x = -11\)[/tex]