Let's solve the inequality step by step.

The inequality is: $2x - 2 < 2(x - 3)$

Step 1: Distribute the 2 on the right side of the inequality.

$2x - 2 < 2x - 6$

Step 2: Subtract $2x$ from both sides.

$-2 < -6$

Step 3: Evaluate the result.

Since $-2$ is not less than $-6$, the inequality $-2 < -6$ is false.

Conclusion:

There are no values of $x$ that satisfy this inequality, so the solution is the empty set.

Final Answer:

• No solution.

Would you like more details on the steps or have any questions?

Here are some related questions you might find useful:

1. How do you solve inequalities with absolute values?
2. What are the rules for multiplying or dividing inequalities by a negative number?
3. How do you solve compound inequalities?
4. What is the difference between solving an equation and solving an inequality?
5. Can you provide an example of solving a quadratic inequality?

Tip: When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number.