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------------------------------------------------ Solve for [tex]x[/tex] in the equation [tex]5|x+9|=80[/tex].

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]

Certainly! Let's solve the equation [tex]$5|x+9|=80$[/tex] step by step.

1. Divide both sides by 5:

Start with the equation:
[tex]\[
5|x + 9| = 80
\][/tex]
Divide both sides by 5 to isolate the absolute value:
[tex]\[
|x + 9| = \frac{80}{5} = 16
\][/tex]

2. Set up two separate equations:

The absolute value equation [tex]$ |x + 9| = 16 $[/tex] gives us two possible equations:
- [tex]$ x + 9 = 16 $[/tex]
- [tex]$ x + 9 = -16 $[/tex]

3. Solve each equation for [tex]$ x $[/tex]:

- For the first equation [tex]$ x + 9 = 16 $[/tex]:
[tex]\[
x = 16 - 9 = 7
\][/tex]

- For the second equation [tex]$ x + 9 = -16 $[/tex]:
[tex]\[
x = -16 - 9 = -25
\][/tex]

4. Conclusion:

The solutions to the equation [tex]$ 5|x+9|=80 $[/tex] are [tex]$ x = 7 $[/tex] and [tex]$ x = -25 $[/tex].

Therefore, the correct answer is [tex]$ x = -25 $[/tex] or [tex]$ x = 7 $[/tex], which corresponds to option D.