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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!

Learn how to solve the linear equation x/2 + 2/5 = 5/6 with a detailed step-by-step solution. This problem involves basic algebraic concepts such as subtracting fractions and isolating variables. Suitable for students in Grades 7-9.

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