College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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]

Answer :

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.