Solve the inequality.
2 x minus 2 less than 2 left parenthesis x minus 3 right parenthesis
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.


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.

Solve the inequality. 2x - 2 < 2(x - 3). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Explore how to solve the inequality 2x - 2 < 2(x - 3) with a detailed step-by-step solution. This problem involves key algebraic concepts such as the distributive property and properties of inequalities, making it suitable for students in Grades 8-10.

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