Answer :
To solve the equation [tex]\(5|x+9|=80\)[/tex], we need to follow these steps:
1. Isolate the Absolute Value:
First, we divide both sides of the equation by 5 to simplify it:
[tex]\[
|x + 9| = \frac{80}{5} = 16
\][/tex]
2. Set Up Two Equations:
The absolute value equation [tex]\(|x + 9| = 16\)[/tex] results in two separate equations because an absolute value can be positive or negative:
[tex]\[
x + 9 = 16 \quad \text{or} \quad x + 9 = -16
\][/tex]
3. Solve Each Equation:
- For [tex]\(x + 9 = 16\)[/tex]:
[tex]\[
x = 16 - 9 = 7
\][/tex]
- For [tex]\(x + 9 = -16\)[/tex]:
[tex]\[
x = -16 - 9 = -25
\][/tex]
4. Write the Solutions:
The solutions to the equation are [tex]\(x = 7\)[/tex] and [tex]\(x = -25\)[/tex].
So, the correct answer is:
B. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex]
1. Isolate the Absolute Value:
First, we divide both sides of the equation by 5 to simplify it:
[tex]\[
|x + 9| = \frac{80}{5} = 16
\][/tex]
2. Set Up Two Equations:
The absolute value equation [tex]\(|x + 9| = 16\)[/tex] results in two separate equations because an absolute value can be positive or negative:
[tex]\[
x + 9 = 16 \quad \text{or} \quad x + 9 = -16
\][/tex]
3. Solve Each Equation:
- For [tex]\(x + 9 = 16\)[/tex]:
[tex]\[
x = 16 - 9 = 7
\][/tex]
- For [tex]\(x + 9 = -16\)[/tex]:
[tex]\[
x = -16 - 9 = -25
\][/tex]
4. Write the Solutions:
The solutions to the equation are [tex]\(x = 7\)[/tex] and [tex]\(x = -25\)[/tex].
So, the correct answer is:
B. [tex]\(x = -25\)[/tex] or [tex]\(x = 7\)[/tex]
