You provided an equation that looks like this:

$\frac{x}{2} + \frac{2}{5} = \frac{5}{6}$

Let's solve it step by step.

Step 1: Isolate the variable term

First, subtract $\frac{2}{5}$ from both sides:

$\frac{x}{2} = \frac{5}{6} - \frac{2}{5}$

Step 2: Find a common denominator for the fractions

The denominators are 6 and 5, so the least common denominator is 30.

$\frac{5}{6} = \frac{25}{30}, \quad \frac{2}{5} = \frac{12}{30}$

Now, subtract the fractions:

$\frac{25}{30} - \frac{12}{30} = \frac{13}{30}$

So we have:

$\frac{x}{2} = \frac{13}{30}$

Step 3: Solve for $x$

To solve for $x$, multiply both sides of the equation by 2:

$x = 2 \times \frac{13}{30} = \frac{26}{30} = \frac{13}{15}$

Final Answer:

$x = \frac{13}{15}$

Let me know if you'd like further clarification!

Here are 5 related questions to practice:

1. Solve $\frac{x}{3} + \frac{1}{4} = \frac{7}{12}$.
2. What is the solution to $\frac{x}{5} + \frac{3}{4} = \frac{7}{8}$?
3. Simplify $\frac{5}{6} - \frac{2}{5}$.
4. If $\frac{y}{4} - \frac{1}{6} = \frac{5}{12}$, find $y$.
5. Solve the equation $\frac{2x}{7} + \frac{3}{5} = \frac{10}{7}$.

Tip: Always simplify fractions to their lowest terms for a cleaner solution!