To solve the inequality:

\[
4x + 2 < 3x - 3
\]

### Step 1: Subtract \(3x\) from both sides to get rid of \(x\) on the right side.

\[
4x - 3x + 2 < -3
\]

This simplifies to:

\[
x + 2 < -3
\]

### Step 2: Subtract 2 from both sides to isolate \(x\).

\[
x < -3 - 2
\]

Simplifying further:

\[
x < -5
\]

### Final Answer:
\[
x < -5
\]

This means that \(x\) must be less than \(-5\) to satisfy the inequality.

Would you like a detailed explanation of any step, or do you have questions?

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Here are five related questions:
1. How would you solve \(5x + 4 > 2x + 7\)?
2. What happens when you multiply or divide an inequality by a negative number?
3. How would you solve a compound inequality like \(3x - 1 < 5 \text{ and } x + 2 > 0\)?
4. Can you solve \(2(x + 3) < 5x - 9\)?
5. How do you graph \(x < -5\) on a number line?

**Tip:** Always reverse the inequality sign when multiplying or dividing both sides by a negative number.

Learn how to solve the linear inequality 4x + 2 < 3x - 3 step-by-step. This tutorial covers essential algebraic concepts, including solving linear inequalities, isolating variables, and applying inequality properties. Suitable for students in Grades 6-8.

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