Answer :
To solve the equation [tex]\(5|x+9| = 80\)[/tex], we need to follow these steps:
1. Divide Both Sides by 5:
First, we simplify the equation by dividing both sides by 5:
[tex]\[
|x+9| = \frac{80}{5} = 16
\][/tex]
2. Consider Two Cases for the Absolute Value:
Since we have an absolute value equation [tex]\(|x+9| = 16\)[/tex], we need to consider two possible cases:
- Case 1: [tex]\(x+9 = 16\)[/tex]
- Case 2: [tex]\(x+9 = -16\)[/tex]
3. Solve Case 1:
For the equation [tex]\(x+9 = 16\)[/tex], we solve for [tex]\(x\)[/tex] by subtracting 9 from both sides:
[tex]\[
x = 16 - 9 = 7
\][/tex]
4. Solve Case 2:
For the equation [tex]\(x+9 = -16\)[/tex], we solve for [tex]\(x\)[/tex] by subtracting 9 from both sides:
[tex]\[
x = -16 - 9 = -25
\][/tex]
5. Write the Final Solution:
The solutions for the equation [tex]\(5 |x+9| = 80\)[/tex] are:
[tex]\[
x = 7 \quad \text{or} \quad x = -25
\][/tex]
So, the correct answer is B. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex].
1. Divide Both Sides by 5:
First, we simplify the equation by dividing both sides by 5:
[tex]\[
|x+9| = \frac{80}{5} = 16
\][/tex]
2. Consider Two Cases for the Absolute Value:
Since we have an absolute value equation [tex]\(|x+9| = 16\)[/tex], we need to consider two possible cases:
- Case 1: [tex]\(x+9 = 16\)[/tex]
- Case 2: [tex]\(x+9 = -16\)[/tex]
3. Solve Case 1:
For the equation [tex]\(x+9 = 16\)[/tex], we solve for [tex]\(x\)[/tex] by subtracting 9 from both sides:
[tex]\[
x = 16 - 9 = 7
\][/tex]
4. Solve Case 2:
For the equation [tex]\(x+9 = -16\)[/tex], we solve for [tex]\(x\)[/tex] by subtracting 9 from both sides:
[tex]\[
x = -16 - 9 = -25
\][/tex]
5. Write the Final Solution:
The solutions for the equation [tex]\(5 |x+9| = 80\)[/tex] are:
[tex]\[
x = 7 \quad \text{or} \quad x = -25
\][/tex]
So, the correct answer is B. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex].
