https://file.aiquickdraw.com/mathbot/file/1726736907333lgl7f7x3.jpg

The equation given in the image is:

\[
\frac{5x}{6} - \frac{1}{2} = \frac{1}{3}
\]

Let's solve this step by step:

### Step 1: Eliminate the fractions
To eliminate the fractions, find the least common denominator (LCD) of 6, 2, and 3. The LCD is 6.

Multiply both sides of the equation by 6:

\[
6 \times \left(\frac{5x}{6} - \frac{1}{2}\right) = 6 \times \frac{1}{3}
\]

This simplifies to:

\[
5x - 3 = 2
\]

### Step 2: Solve for \( x \)
Now, add 3 to both sides:

\[
5x = 2 + 3
\]
\[
5x = 5
\]

Finally, divide both sides by 5:

\[
x = \frac{5}{5}
\]
\[
x = 1
\]

### Solution:
The value of \( x \) is \( 1 \).

Would you like further details or explanations on any step? 

Here are 5 related questions for practice:
1. What is the solution to \( \frac{3x}{4} - \frac{2}{3} = \frac{1}{2} \)?
2. How would the equation change if the right-hand side were \( \frac{2}{3} \) instead of \( \frac{1}{3} \)?
3. Solve \( \frac{7x}{5} + \frac{3}{4} = \frac{1}{2} \).
4. What happens to the solution if we multiply both sides of the original equation by 12 instead of 6?
5. How do you solve \( \frac{x}{2} - \frac{5}{3} = \frac{4}{3} \)?

Tip: When solving rational equations, eliminating fractions early by multiplying through by the least common denominator can simplify the process.

What is the value of x of the rational equation \(\frac{5x}{6} - \frac{1}{2} = \frac{1}{3}\)?

Learn how to solve the rational equation \(\frac{5x}{6} - \frac{1}{2} = \frac{1}{3}\) step by step. This problem involves finding the least common denominator (LCD) and solving for x. Ideal for students in Grades 7-9.

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