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.

Learn how to solve the linear equation 3(x+2)-2(x-5)=10 with a step-by-step breakdown. This problem covers key algebraic concepts, including the distributive property and combining like terms. Suitable for students in Grades 6-8.

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