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The image contains a mathematical expression that appears to involve simplifying or solving an equation using parentheses and fractions. Here is the transcription of the expression:

\[
\left(\frac{4}{5}\right)(5x - 4) = \left(\frac{5}{4}\right)(4x - 5)
\]

To solve this equation, we can begin by distributing the fractions on both sides.

1. Distribute \(\frac{4}{5}\) on the left-hand side:
   \[
   \frac{4}{5}(5x - 4) = \frac{4}{5}(5x) - \frac{4}{5}(4)
   \]
   This simplifies to:
   \[
   4x - \frac{16}{5}
   \]

2. Distribute \(\frac{5}{4}\) on the right-hand side:
   \[
   \frac{5}{4}(4x - 5) = \frac{5}{4}(4x) - \frac{5}{4}(5)
   \]
   This simplifies to:
   \[
   5x - \frac{25}{4}
   \]

Now, the equation becomes:
\[
4x - \frac{16}{5} = 5x - \frac{25}{4}
\]

Next, we will eliminate the fractions by multiplying the entire equation by the least common denominator (LCD) of 5 and 4, which is 20:

\[
20 \left(4x - \frac{16}{5}\right) = 20 \left(5x - \frac{25}{4}\right)
\]

This gives:
\[
80x - 64 = 100x - 125
\]

Now, we can simplify and solve for \(x\):

1. Subtract \(80x\) from both sides:
   \[
   -64 = 20x - 125
   \]

2. Add 125 to both sides:
   \[
   61 = 20x
   \]

3. Divide by 20:
   \[
   x = \frac{61}{20}
   \]

Thus, the solution to the equation is \(x = \frac{61}{20}\).

Would you like more details or have any questions?

Here are five related questions:
1. How do we handle equations with fractions more generally?
2. Why is it important to eliminate fractions when solving equations?
3. What other methods can we use to solve equations with variables on both sides?
4. How can we check if the solution \(x = \frac{61}{20}\) is correct?
5. Can this equation be solved graphically?

**Tip:** Always check your final solution by substituting it back into the original equation.

Solve the equation (4/5)(5x - 4) = (5/4)(4x - 5)

This problem involves solving a linear equation with fractions. The equation (4/5)(5x - 4) = (5/4)(4x - 5) is solved step-by-step using the distributive property and eliminating fractions. Suitable for students in Grades 9-11.

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