College

Solve [tex]$4|x+5|=28$[/tex].

A. [tex]$x=-12$[/tex] and [tex][tex]$x=2$[/tex][/tex]
B. [tex]$x=12$[/tex] and [tex]$x=-2$[/tex]
C. [tex][tex]$x=12$[/tex][/tex] and [tex]$x=-12$[/tex]
D. [tex]$x=-12$[/tex] and [tex][tex]$x=-2$[/tex][/tex]

Answer :

To solve the equation [tex]\(4|x+5|=28\)[/tex], follow these steps:

1. Isolate the Absolute Value:
- Start by dividing both sides of the equation by 4 to isolate the absolute value:
[tex]\[
|x+5| = \frac{28}{4} = 7
\][/tex]

2. Set Up the Two Cases for the Absolute Value:
- The expression [tex]\( |x+5| = 7 \)[/tex] means that [tex]\( x+5 \)[/tex] can either be 7 or -7. So, we have two cases to consider:
- Case 1: [tex]\( x + 5 = 7 \)[/tex]
- Case 2: [tex]\( x + 5 = -7 \)[/tex]

3. Solve for [tex]\( x \)[/tex] in Each Case:

- Case 1:
[tex]\[
x + 5 = 7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 7 - 5 = 2
\][/tex]

- Case 2:
[tex]\[
x + 5 = -7
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -7 - 5 = -12
\][/tex]

4. Write the Solutions:
- The solutions to the equation [tex]\(4|x+5|=28\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = -12\)[/tex].

Based on these steps, the correct answer is option A: [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex].