It looks like you have an equation to solve. However, the equation is presented twice and is slightly unclear. I will take it as one equation that you want to simplify and solve. Let's clarify the expression:

We want to solve the following:

\[
\frac{5}{2}x - \frac{1}{3}x + 2 = 3
\]

Let's solve this step-by-step.

1. Combine the terms on the left side:
\[
\frac{5}{2}x - \frac{1}{3}x + 2 = 3
\]

2. Find a common denominator to combine \(\frac{5}{2}x\) and \(-\frac{1}{3}x\). The common denominator for 2 and 3 is 6.

- Convert \(\frac{5}{2}x\) to sixths:
\[
\frac{5}{2}x = \frac{15}{6}x
\]

- Convert \(-\frac{1}{3}x\) to sixths:
\[
-\frac{1}{3}x = -\frac{2}{6}x
\]

3. Now, add these fractions:
\[
\frac{15}{6}x - \frac{2}{6}x = \frac{13}{6}x
\]

4. Substitute back into the equation:
\[
\frac{13}{6}x + 2 = 3
\]

5. To isolate \(x\), subtract 2 from both sides:
\[
\frac{13}{6}x = 3 - 2
\]
\[
\frac{13}{6}x = 1
\]

6. Multiply both sides by the reciprocal of \(\frac{13}{6}\):
\[
x = 1 \cdot \frac{6}{13}
\]
\[
x = \frac{6}{13}
\]

So, the solution to the equation is:
\[
\boxed{\frac{6}{13}}
\]