High School

Select the correct answer.

Solve: [tex]5|x+9|=80[/tex]

A. [tex]x=-25[/tex] or [tex]x=7[/tex]
B. [tex]x=-7[/tex] or [tex]x=25[/tex]
C. [tex]x=7[/tex] or [tex]x=16[/tex]
D. [tex]x=-25[/tex] or [tex]x=9[/tex]

Answer :

To solve the equation [tex]\(5|x+9| = 80\)[/tex], we'll need to handle the absolute value carefully. Here's a step-by-step solution:

1. Isolate the Absolute Value: Divide both sides of the equation by 5 to simplify it:
[tex]\[
|x + 9| = \frac{80}{5}
\][/tex]
[tex]\[
|x + 9| = 16
\][/tex]

2. Consider the Two Cases Involving Absolute Value: The expression inside the absolute value can be either positive or negative. So, set up two separate equations:

- Case 1: [tex]\(x + 9 = 16\)[/tex]
- Case 2: [tex]\(-(x + 9) = 16\)[/tex]

3. Solve Each Case:

- For Case 1:
[tex]\[
x + 9 = 16
\][/tex]
Subtract 9 from both sides:
[tex]\[
x = 16 - 9
\][/tex]
[tex]\[
x = 7
\][/tex]

- For Case 2:
[tex]\[
-(x + 9) = 16
\][/tex]
Multiplying both sides by -1 gives:
[tex]\[
x + 9 = -16
\][/tex]
Subtract 9 from both sides:
[tex]\[
x = -16 - 9
\][/tex]
[tex]\[
x = -25
\][/tex]

4. Check the Solutions: We found two possible solutions for [tex]\(x\)[/tex]: [tex]\(x = 7\)[/tex] and [tex]\(x = -25\)[/tex]. Plugging these back into the original equation confirms they work because both satisfy [tex]\(5|x+9| = 80\)[/tex].

Therefore, the correct answer is:

A. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex]

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