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The inequality you provided is:

\[
4 - 2x < 9 - 3x
\]

Let's solve it step by step:

### Step 1: Simplify both sides
We can move the terms involving \(x\) to one side and the constants to the other.

First, add \(3x\) to both sides to eliminate the \(-3x\) on the right-hand side:

\[
4 - 2x + 3x < 9 - 3x + 3x
\]

This simplifies to:

\[
4 + x < 9
\]

### Step 2: Isolate \(x\)
Now, subtract 4 from both sides to isolate \(x\):

\[
x < 9 - 4
\]

\[
x < 5
\]

### Final Solution:
The solution to the inequality is:

\[
x < 5
\]

This means that \(x\) can take any value less than 5.

Would you like more details, or do you have any questions about the steps?

### Related Questions:
1. How would you solve the inequality \(3x - 7 \leq 2x + 1\)?
2. Can you explain the difference between solving equations and inequalities?
3. How do the rules change if you multiply or divide an inequality by a negative number?
4. What would be the graphical representation of \(x < 5\) on a number line?
5. How do you check if a specific value of \(x\) satisfies an inequality?

### Tip:
Remember, when solving inequalities, if you multiply or divide both sides by a negative number, you must reverse the inequality sign.

Learn how to solve the linear inequality 4 - 2x < 9 - 3x with a detailed step-by-step explanation. This problem involves key algebraic concepts such as inequality manipulation and variable isolation. Suitable for students in Grades 7-9.

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