To solve the equation [tex]\(\frac{x + 8}{3} = \frac{x - 3}{2}\)[/tex], follow these steps:
1. Clear the Fractions:
To eliminate the fractions, multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 6.
[tex]\[
6 \cdot \frac{x + 8}{3} = 6 \cdot \frac{x - 3}{2}
\][/tex]
2. Simplify the Equation:
Multiply through and simplify:
[tex]\[
6 \cdot \frac{x + 8}{3} = (6 \div 3) \cdot (x + 8) = 2(x + 8)
\][/tex]
[tex]\[
6 \cdot \frac{x - 3}{2} = (6 \div 2) \cdot (x - 3) = 3(x - 3)
\][/tex]
So, the equation simplifies to:
[tex]\[
2(x + 8) = 3(x - 3)
\][/tex]
3. Distribute:
Distribute the constants through the parentheses:
[tex]\[
2x + 16 = 3x - 9
\][/tex]
4. Combine Like Terms:
First, get all x terms on one side by subtracting 2x from both sides:
[tex]\[
16 = x - 9
\][/tex]
Then add 9 to both sides to isolate x:
[tex]\[
16 + 9 = x
\][/tex]
[tex]\[
25 = x
\][/tex]
5. State the Solution:
The solution to the equation is:
[tex]\[
x = 25
\][/tex]
Therefore, the correct choice is:
A. The solution is [tex]\( x = 25 \)[/tex].
