To solve the equation $5(x - 2) - 3x = 2(x - 5)$, follow these steps:

1. Distribute the constants on both sides of the equation:

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

This becomes:

$5x - 10 - 3x = 2x - 10$

2. Combine like terms on both sides:

$(5x - 3x) - 10 = 2x - 10$

Simplifying, we get:

$2x - 10 = 2x - 10$

3. At this point, we notice that the equation $2x - 10 = 2x - 10$ is an identity, meaning it is true for all values of $x$. This indicates that there is no single solution; instead, every value of $x$ satisfies the equation.

So, the equation has infinitely many solutions.

Would you like more details or have any questions about this solution?

Here are some related questions for further practice:

1. Solve for $x$: $3(x - 4) - 2x = 5(x - 6)$.
2. If $7(x - 1) - 4x = 3(x - 3)$, what is the value of $x$?
3. Solve the equation: $4(x - 2) - 3x = 5(x - 5)$.
4. What is $x$ if $6(x - 3) - 2x = 4(x - 7)$?
5. If $8(x - 4) - 5x = 6(x - 8)$, find $x$.
6. Solve for $x$: $9(x - 5) - 3x = 7(x - 9)$.
7. If $10(x - 6) - 4x = 8(x - 10)$, what is $x$?
8. Solve the equation: $11(x - 7) - 5x = 9(x - 11)$.

Tip: Always check if the equation simplifies to an identity, as this can indicate that the equation is true for all values of $x$.