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Solve the equation:

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

Choose the correct solution:

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

Answer :

To solve the equation [tex]\(5|x+9| = 80\)[/tex], we will follow these steps:

1. Divide both sides by 5:
[tex]\[
|x+9| = \frac{80}{5} = 16
\][/tex]

2. Set up the two possible cases for the absolute value expression:

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

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

4. Solve Case 2:
[tex]\[
x + 9 = -16
\][/tex]
Subtract 9 from both sides:
[tex]\[
x = -16 - 9 = -25
\][/tex]

Therefore, the solutions to the equation [tex]\(5|x+9| = 80\)[/tex] are [tex]\(x = 7\)[/tex] and [tex]\(x = -25\)[/tex].

Looking at the provided options, the correct choice is:
D. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex]

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