College

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

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

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

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

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

Answer :

Sure, let's solve the equation [tex]\(4|x + 6| + 8 = 28\)[/tex] step by step.

### Step 1: Isolate the Absolute Value Expression

First, let's subtract 8 from both sides of the equation to simplify it.

[tex]\[
4|x + 6| + 8 - 8 = 28 - 8
\][/tex]

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

### Step 2: Solve for the Absolute Value

Next, we divide both sides by 4.

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

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

### Step 3: Set Up Two Equations

The absolute value [tex]\( |x + 6| = 5 \)[/tex] means that [tex]\( x + 6 \)[/tex] can be 5 or -5. Therefore, we set up two separate equations:

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

### Step 4: Solve Each Equation

For the first equation:

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

Subtract 6 from both sides:

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

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

For the second equation:

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

Subtract 6 from both sides:

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

[tex]\[
x = -11
\][/tex]

### Step 5: List the Solutions

The solutions to the equation [tex]\(4|x + 6| + 8 = 28\)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -11 \)[/tex].

So, the correct answer is:

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