Final answer:
The compound inequality 'X - 5 < 3' OR 'X - 5 ≥ 29' has solutions where X is less than 8 or greater than or equal to 34. The graphed solutions show shaded regions to the left of 8 and to the right of 34 on a number line, with an open circle at 8 and a closed circle at 34.
Step-by-step explanation:
To solve the compound inequality and graph the solutions for the given inequalities 'X - 5 < 3' OR 'X - 5 ≥ 29', we first solve each inequality separately:
- For X - 5 < 3, add 5 to both sides to get X < 8.
- For X - 5 ≥ 29, add 5 to both sides to get X ≥ 34.
The solution to the compound inequality is the union of the solutions to the individual inequalities, which means X is either less than 8 or greater than or equal to 34. To graph these solutions:
- Draw a number line.
- Put an open circle at 8, indicating that 8 is not included in the solution.
- Shade the line to the left of 8, showing all numbers less than 8.
- Put a closed circle at 34, indicating that 34 is included in the solution.
- Shade the line to the right of 34, showing all numbers greater than or equal to 34.
The shaded regions represent the solution to the compound inequality. There is no upper or lower limit to the shading on the left of 8 and on the right of 34.