Answer :
To solve the equation [tex]\(5|x+9|=80\)[/tex], we can follow these steps:
1. Divide both sides by 5:
[tex]\[
|x+9| = \frac{80}{5}
\][/tex]
[tex]\[
|x+9| = 16
\][/tex]
2. Consider the two possible cases for the absolute value equation:
- Case 1: [tex]\(x + 9 = 16\)[/tex]
[tex]\[
x = 16 - 9
\][/tex]
[tex]\[
x = 7
\][/tex]
- Case 2: [tex]\(x + 9 = -16\)[/tex]
[tex]\[
x = -16 - 9
\][/tex]
[tex]\[
x = -25
\][/tex]
So, the solutions for the equation are [tex]\(x = 7\)[/tex] and [tex]\(x = -25\)[/tex].
3. Select the correct answer from the options provided:
- A. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex]
Therefore, the correct answer is A. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex].
1. Divide both sides by 5:
[tex]\[
|x+9| = \frac{80}{5}
\][/tex]
[tex]\[
|x+9| = 16
\][/tex]
2. Consider the two possible cases for the absolute value equation:
- Case 1: [tex]\(x + 9 = 16\)[/tex]
[tex]\[
x = 16 - 9
\][/tex]
[tex]\[
x = 7
\][/tex]
- Case 2: [tex]\(x + 9 = -16\)[/tex]
[tex]\[
x = -16 - 9
\][/tex]
[tex]\[
x = -25
\][/tex]
So, the solutions for the equation are [tex]\(x = 7\)[/tex] and [tex]\(x = -25\)[/tex].
3. Select the correct answer from the options provided:
- A. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex]
Therefore, the correct answer is A. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex].
