Question

8/2 + 3x /2 = 13 + x , one solution; no solution

Answer 1

To solve the equation \( \frac{8}{2} + \frac{3x}{2} = 13 + x \), let's simplify and rearrange the equation step by step:

1. Simplify \( \frac{8}{2} \):
\[
4 + \frac{3x}{2} = 13 + x
\]

2. Next, let's eliminate the fraction by multiplying the entire equation by 2:
\[
2 \cdot 4 + 2 \cdot \frac{3x}{2} = 2 \cdot (13 + x)
\]
\[
8 + 3x = 26 + 2x
\]

3. Now, isolate \(x\) by subtracting \(2x\) from both sides:
\[
8 + 3x - 2x = 26
\]
\[
8 + x = 26
\]

4. Then subtract 8 from both sides:
\[
x = 26 - 8
\]
\[
x = 18
\]

So, the solution to the equation is \(x = 18\). Since this is a single solution, we can conclude that the equation has one solution.