We need to solve the equation $\frac{5x}{2} - 7 = \frac{2x - 7}{6}$ for $x$.

1. Problem Description

We need to solve the equation $\frac{5x}{2} - 7 = \frac{2x - 7}{6}$ for $x$.

2. Solution Steps

To solve the equation, we first eliminate the fractions by multiplying both sides by the least common multiple of 2 and 6, which is

6. $$6\left(\frac{5x}{2} - 7\right) = 6\left(\frac{2x - 7}{6}\right)$$

$$6\left(\frac{5x}{2}\right) - 6(7) = 2x - 7$$

$$3(5x) - 42 = 2x - 7$$

$$15x - 42 = 2x - 7$$

Now, we isolate the $x$ terms by subtracting $2x$ from both sides.

$$15x - 2x - 42 = 2x - 2x - 7$$

$$13x - 42 = -7$$

Next, we isolate the $x$ term by adding 42 to both sides.

$$13x - 42 + 42 = -7 + 42$$

$$13x = 35$$

Finally, we solve for $x$ by dividing both sides by

1

3. $$\frac{13x}{13} = \frac{35}{13}$$

$$x = \frac{35}{13}$$

3. Final Answer

The solution to the equation is $x = \frac{35}{13}$.