Solve the compound inequality.
3x-1>2 or 4x+5 less than or equal to -19
Graph the solution on the number line.

Let's solve each part of the compound inequality step by step.

### Part 1: Solve \( 3x - 1 > 2 \)

1. Add 1 to both sides:
   \[
   3x > 3
   \]
2. Divide by 3:
   \[
   x > 1
   \]

### Part 2: Solve \( 4x + 5 \leq -19 \)

1. Subtract 5 from both sides:
   \[
   4x \leq -24
   \]
2. Divide by 4:
   \[
   x \leq -6
   \]

### Compound Inequality
The compound inequality is:
\[
x > 1 \quad \text{or} \quad x \leq -6
\]

This means the solution includes any \(x\) greater than 1 **or** any \(x\) less than or equal to -6.

### Graphing the Solution

On a number line:
- For \(x > 1\), use an open circle at 1 and shade to the right (greater than 1).
- For \(x \leq -6\), use a closed circle at -6 and shade to the left (less than or equal to -6).

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### 5 Related Questions:
1. What is the difference between solving "or" and "and" inequalities?
2. How do you graph inequalities with both open and closed circles?
3. What happens if an inequality has no solution?
4. Can inequalities be solved with variables on both sides?
5. How do absolute value inequalities differ from regular inequalities?

### Tip: Always check your solution by plugging values back into the original inequalities!

Solve the compound inequality. 3x - 1 > 2 or 4x + 5 ≤ -19. Graph the solution on the number line.

Learn how to solve and graph the compound inequality 3x - 1 > 2 or 4x + 5 ≤ -19. This step-by-step guide covers solving inequalities, understanding 'or' conditions, and graphing the solution on a number line. Suitable for students in Grades 8-10.

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