High School

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]$x=2$[/tex]

D. [tex]$x=12$[/tex] and [tex][tex]$x=-12$[/tex][/tex]

Answer :

To solve the equation [tex]\(4|x+5|=28\)[/tex], let's go through the steps one by one:

1. Isolate the absolute value expression:

Start with the equation:
[tex]\[
4|x+5| = 28
\][/tex]

Divide both sides by 4 to simplify:
[tex]\[
|x+5| = 7
\][/tex]

2. Consider the two cases for the absolute value:

An absolute value equation like [tex]\(|x+5| = 7\)[/tex] means that [tex]\(x+5\)[/tex] can be either 7 or -7.

- Case 1: [tex]\(x+5 = 7\)[/tex]
- Case 2: [tex]\(x+5 = -7\)[/tex]

3. Solve each case:

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

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

4. Conclusion:

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

Therefore, the correct answer is Option C: [tex]\(x = -12\)[/tex] and [tex]\(x = 2\)[/tex].

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