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Answer :
To solve the equation [tex]\(5|x+9| = 80\)[/tex], follow these steps:
1. Isolate the absolute value:
Start by dividing both sides of the equation by 5. This will help to simplify the equation and isolate the absolute value term.
[tex]\[
|x+9| = \frac{80}{5} = 16
\][/tex]
2. Solve the equation inside the absolute value:
An equation involving absolute value, such as [tex]\(|x+9| = 16\)[/tex], means that the expression inside the absolute value can either be equal to 16 or -16. Therefore, we set up two separate equations to solve:
- First equation: [tex]\(x+9 = 16\)[/tex]
[tex]\[
x = 16 - 9 = 7
\][/tex]
- Second equation: [tex]\(x+9 = -16\)[/tex]
[tex]\[
x = -16 - 9 = -25
\][/tex]
3. State the solutions:
The solutions to the equation [tex]\(5|x+9| = 80\)[/tex] are [tex]\(x = 7\)[/tex] and [tex]\(x = -25\)[/tex].
Hence, the correct answer is A. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex].
1. Isolate the absolute value:
Start by dividing both sides of the equation by 5. This will help to simplify the equation and isolate the absolute value term.
[tex]\[
|x+9| = \frac{80}{5} = 16
\][/tex]
2. Solve the equation inside the absolute value:
An equation involving absolute value, such as [tex]\(|x+9| = 16\)[/tex], means that the expression inside the absolute value can either be equal to 16 or -16. Therefore, we set up two separate equations to solve:
- First equation: [tex]\(x+9 = 16\)[/tex]
[tex]\[
x = 16 - 9 = 7
\][/tex]
- Second equation: [tex]\(x+9 = -16\)[/tex]
[tex]\[
x = -16 - 9 = -25
\][/tex]
3. State the solutions:
The solutions to the equation [tex]\(5|x+9| = 80\)[/tex] are [tex]\(x = 7\)[/tex] and [tex]\(x = -25\)[/tex].
Hence, the correct answer is A. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex].
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