To solve the inequality \(2(1 - 3x) < 20\), follow these steps:

1. **Distribute the 2** to both terms inside the parentheses:

   \[
   2 \cdot 1 - 2 \cdot 3x < 20
   \]

   This simplifies to:

   \[
   2 - 6x < 20
   \]

2. **Isolate the term with \(x\)**. First, subtract 2 from both sides:

   \[
   -6x < 20 - 2
   \]

   Simplifying gives:

   \[
   -6x < 18
   \]

3. **Solve for \(x\)** by dividing both sides by \(-6\). Remember, when you divide or multiply by a negative number in an inequality, the inequality sign flips:

   \[
   x > \frac{18}{-6}
   \]

   Simplifying:

   \[
   x > -3
   \]

The solution to the inequality is \(x > -3\).

Would you like any details or have any questions?

Here are five related questions you might find interesting:
1. How do you solve inequalities that involve fractions?
2. What happens to the inequality sign when you multiply or divide by a negative number?
3. How do you represent the solution to an inequality on a number line?
4. What is the difference between solving an equation and solving an inequality?
5. How do you check if a solution to an inequality is correct?

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

Learn how to solve the linear inequality 2(1 - 3x) < 20 with this step-by-step solution. This problem covers key algebraic concepts such as the distributive property and handling inequalities when dividing by negative numbers. Perfect for students in Grades 7-9.

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