https://file.aiquickdraw.com/mathbot/file/1725837597196u7wj2pvd.jpg

The problem shown in the image is:

\[
\frac{5}{6}x - \frac{1}{5}x = 19
\]

We can solve this equation step by step.

### Step 1: Combine like terms.
Since both terms involve \(x\), you can combine them by getting a common denominator.

The common denominator between 6 and 5 is 30.

- Convert \(\frac{5}{6}\) to \(\frac{25}{30}\)
- Convert \(\frac{1}{5}\) to \(\frac{6}{30}\)

So, the equation becomes:

\[
\frac{25}{30}x - \frac{6}{30}x = 19
\]

### Step 2: Simplify the left-hand side.

\[
\frac{25 - 6}{30}x = 19
\]

\[
\frac{19}{30}x = 19
\]

### Step 3: Solve for \(x\).

Multiply both sides by the reciprocal of \(\frac{19}{30}\), which is \(\frac{30}{19}\):

\[
x = 19 \times \frac{30}{19}
\]

\[
x = 30
\]

Thus, the solution is:

\[
x = 30
\]

Would you like more details on any of these steps?

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Here are 5 related questions to extend your learning:
1. How would you solve if the equation was \(\frac{5}{6}x + \frac{1}{5}x = 19\)?
2. Can you apply the same method if the equation involved fractions with larger denominators?
3. What would happen if the constant on the right side was negative, say \(-19\)?
4. How can you solve this equation by multiplying both sides by the least common denominator from the start?
5. How would the steps differ if the equation were quadratic instead of linear?

**Tip:** Always check your final answer by substituting it back into the original equation to ensure it satisfies the equation.

Complete the steps to solve for x: (5/6)x - (1/5)x = 19

Learn how to solve the linear equation (5/6)x - (1/5)x = 19 with step-by-step instructions. This problem involves combining fractions, simplifying, and solving for x using fundamental algebraic principles. Suitable for students in Grades 7-9.

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