The inequality is:

\[
-2x < -6
\]

To solve for \( x \), follow these steps:

1. Divide both sides of the inequality by \(-2\). **Remember**, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign must be **reversed**.

\[
x > \frac{-6}{-2}
\]

2. Simplify:

\[
x > 3
\]

So, the solution is:

\[
x > 3
\]

### Do you want further details or have any questions?

Here are 5 related questions:

1. How would you solve the inequality \(3x - 2 > 7\)?
2. What happens when you multiply or divide both sides of an inequality by zero?
3. Can you solve the inequality \(4 - x \leq 2\)?
4. What is the difference between solving equations and inequalities?
5. How do you graph the solution \(x > 3\) on a number line?

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

Learn how to solve the inequality -2x < -6 with a detailed, step-by-step solution. Understand key algebraic concepts such as inequalities and how dividing by negative numbers affects the inequality sign. Suitable for students in Grades 6-8.

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