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.
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.
