To solve the inequality:

\[
2x - 7 < 4x - 2
\]

1. First, bring all terms involving \( x \) to one side of the inequality. Subtract \( 2x \) from both sides:

   \[
   -7 < 2x - 2
   \]

2. Next, add \( 2 \) to both sides to isolate the term with \( x \):

   \[
   -5 < 2x
   \]

3. Finally, divide both sides by \( 2 \) to solve for \( x \):

   \[
   x > -\frac{5}{2}
   \]

So, the solution is:

\[
x > -\frac{5}{2}
\]

Would you like more details on any step or have any questions?

### Related Questions
1. How would you solve \( 3x - 4 < 2x + 1 \)?
2. How can inequalities change if you multiply or divide by a negative number?
3. What is the solution to \( 5x + 3 > 2x + 9 \)?
4. How would you solve a compound inequality like \( 2x + 3 < 5 \) and \( 3x - 1 > 2 \)?
5. Can you graph \( x > -\frac{5}{2} \) on a number line?

### Tip
When solving inequalities, remember that multiplying or dividing by a negative number reverses the inequality sign.

Learn how to solve the inequality 2x - 7 < 4x - 2 with a clear, step-by-step solution. This algebra problem focuses on the properties of inequalities and linear equations, ideal for students in Grades 8-10.

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