To solve the inequality \( 1 - 4x > 19 \):

1. **Subtract 1 from both sides** to isolate the term involving \(x\):
   \[
   1 - 4x - 1 > 19 - 1
   \]
   This simplifies to:
   \[
   -4x > 18
   \]

2. **Divide both sides by -4**. Since we are dividing by a negative number, **reverse the inequality sign**:
   \[
   x < \frac{18}{-4}
   \]
   Simplifying the fraction:
   \[
   x < -\frac{9}{2} \quad \text{or} \quad x < -4.5
   \]

### Solution: 
\[
x < -4.5
\]

Would you like further details or have any questions?

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Here are 5 related questions:
1. What is the solution set for \( 2 - 3x \geq 7 \)?
2. Solve \( 5x - 9 \leq 2x + 3 \).
3. How do you solve \( -2x + 8 > 4 \)?
4. What happens if you divide an inequality by a negative number?
5. Solve the system of inequalities \( 3x - 2 \leq 4 \) and \( x + 1 > 0 \).

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

Learn how to solve the linear inequality 1 - 4x > 19 with a step-by-step explanation. This problem covers important algebraic concepts, including inequality manipulation and the rule of reversing the inequality when dividing by a negative number. Suitable for students in Grades 8-10.

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