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------------------------------------------------ Select the correct answer.

Solve:

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

A. [tex]x=-25[/tex] or [tex]x=9[/tex]

B. [tex]x=-25[/tex] or [tex]x=7[/tex]

C. [tex]x=7[/tex] or [tex]x=16[/tex]

D. [tex]x=-7[/tex] or [tex]x=25[/tex]

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

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

2. Solve the Absolute Value Equation:
The equation [tex]$|x+9| = 16$[/tex] leads to two cases:

- Case 1: [tex]$x + 9 = 16$[/tex]
Solve for [tex]$x$[/tex] by subtracting 9 from both sides:
[tex]$x = 16 - 9$[/tex]
[tex]$x = 7$[/tex]

- Case 2: [tex]$x + 9 = -16$[/tex]
Solve for [tex]$x$[/tex] by subtracting 9 from both sides:
[tex]$x = -16 - 9$[/tex]
[tex]$x = -25$[/tex]

3. Final Solution:
The solutions for the equation [tex]$5|x+9|=80$[/tex] are [tex]$x = 7$[/tex] and [tex]$x = -25$[/tex].

Therefore, the correct answer is:

B. [tex]$x = -25$[/tex] or [tex]$x = 7$[/tex]