We have the equation:

\[
\frac{2x}{3} - \frac{x}{6} = 10
\]

To solve this, we first eliminate the fractions by finding a common denominator. The least common denominator between 3 and 6 is 6. So, let's rewrite each term:

\[
\frac{2x}{3} = \frac{4x}{6}
\]

Now the equation becomes:

\[
\frac{4x}{6} - \frac{x}{6} = 10
\]

Since both terms on the left have the same denominator, we can combine them:

\[
\frac{4x - x}{6} = 10
\]

Simplifying:

\[
\frac{3x}{6} = 10
\]

This reduces to:

\[
\frac{x}{2} = 10
\]

Now, solve for \(x\) by multiplying both sides by 2:

\[
x = 20
\]

So, the solution is \(x = 20\).

Would you like more details on any step or have any questions?

### Related questions:
1. How do you solve equations with different denominators?
2. What are some other methods to solve linear equations?
3. How do you check your solution in an equation?
4. How do you solve equations involving variables on both sides?
5. What happens if there are no solutions or infinite solutions to an equation?

**Tip:** Always check your final solution by plugging it back into the original equation!

Discover how to solve the linear equation 2x/3 - x/6 = 10 using fractions. This problem covers algebraic techniques for simplifying fractions and solving equations, making it ideal for students in Grades 7-8.

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