Answer :
Let's solve the equation [tex]\(5|x+9|=80\)[/tex] step by step:
1. Isolate the Absolute Value:
Divide both sides of the equation by 5 to get:
[tex]\(|x+9| = \frac{80}{5}\)[/tex]
[tex]\(|x+9| = 16\)[/tex]
2. Solve the Absolute Value Equation:
The equation [tex]\(|x+9| = 16\)[/tex] leads to two cases:
- Case 1: [tex]\(x + 9 = 16\)[/tex]
Solve for [tex]\(x\)[/tex] by subtracting 9 from both sides:
[tex]\(x = 16 - 9\)[/tex]
[tex]\(x = 7\)[/tex]
- Case 2: [tex]\(x + 9 = -16\)[/tex]
Solve for [tex]\(x\)[/tex] by subtracting 9 from both sides:
[tex]\(x = -16 - 9\)[/tex]
[tex]\(x = -25\)[/tex]
3. Final Solution:
The solutions for the equation [tex]\(5|x+9|=80\)[/tex] are [tex]\(x = 7\)[/tex] and [tex]\(x = -25\)[/tex].
Therefore, the correct answer is:
B. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex]
1. Isolate the Absolute Value:
Divide both sides of the equation by 5 to get:
[tex]\(|x+9| = \frac{80}{5}\)[/tex]
[tex]\(|x+9| = 16\)[/tex]
2. Solve the Absolute Value Equation:
The equation [tex]\(|x+9| = 16\)[/tex] leads to two cases:
- Case 1: [tex]\(x + 9 = 16\)[/tex]
Solve for [tex]\(x\)[/tex] by subtracting 9 from both sides:
[tex]\(x = 16 - 9\)[/tex]
[tex]\(x = 7\)[/tex]
- Case 2: [tex]\(x + 9 = -16\)[/tex]
Solve for [tex]\(x\)[/tex] by subtracting 9 from both sides:
[tex]\(x = -16 - 9\)[/tex]
[tex]\(x = -25\)[/tex]
3. Final Solution:
The solutions for the equation [tex]\(5|x+9|=80\)[/tex] are [tex]\(x = 7\)[/tex] and [tex]\(x = -25\)[/tex].
Therefore, the correct answer is:
B. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex]
