Let's solve the equation step by step.

Given:

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

Step 1: Distribute the constants.

Distribute $3$ and $-2$ across their respective parentheses:

$3(x + 2) = 3x + 6$ $-2(x - 5) = -2x + 10$

Now substitute these back into the equation:

$3x + 6 - 2x + 10 = 10$

Step 2: Combine like terms.

Combine $3x$ and $-2x$, and combine the constants $6$ and $10$:

$(3x - 2x) + (6 + 10) = 10$ $x + 16 = 10$

Step 3: Isolate $x$.

Subtract 16 from both sides to isolate $x$:

$x = 10 - 16$ $x = -6$

Final answer:

$x = -6$

Do you want more details or have any questions?

Here are 5 related questions:

1. How would you check if $x = -6$ is the correct solution?
2. What is the next step if you encounter variables on both sides of the equation?
3. How does distributing a negative sign affect the terms inside parentheses?
4. Can this equation be solved using an alternative method like factoring?
5. How would the solution change if the equation was $3(x + 2) + 2(x - 5) = 10$?

Tip: Always distribute any constants outside parentheses before simplifying equations.