To solve the inequality \(10 - 3x > 2x - 5\), follow these steps:

1. **Combine like terms involving \(x\):**
   \[
   10 - 3x > 2x - 5
   \]

   Add \(3x\) to both sides to move all \(x\) terms to one side:
   \[
   10 > 5x - 5
   \]

2. **Isolate the variable term \(5x\):**
   Add 5 to both sides to move the constant term:
   \[
   15 > 5x
   \]

3. **Solve for \(x\):**
   Divide both sides by 5:
   \[
   3 > x
   \]
   or equivalently,
   \[
   x < 3
   \]

So the solution to the inequality is \(x < 3\).

Would you like more details on any part of the solution, or do you have any questions?

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Here are 8 related questions for further practice:

1. Solve the inequality \(4 - 2x > x + 1\).
2. Solve the inequality \(7x - 4 < 3x + 12\).
3. What is the solution set for \(5x + 3 \leq 2x + 9\)?
4. Solve the inequality \(6 - 4x \geq 2x + 10\).
5. What is the solution for \(3x - 7 > 2x - 9\)?
6. Solve \(10x + 15 > 5x + 30\) and express the solution set.
7. What is the solution set for \(8 - 2x < 3x + 2\)?
8. Solve the compound inequality \(4 < 2x - 6 \leq 10\).

**Tip:** When solving inequalities, remember that if you multiply or divide by a negative number, the inequality sign must be reversed.

Learn how to solve the inequality 10 - 3x > 2x - 5 with detailed step-by-step instructions. This problem covers key algebraic concepts including inequalities and linear equations. Suitable for students in Grades 7-9.

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