Final answer:
The correct inequality that can be represented by the number line is option D: 5x - 2 > -22 and 6x - 7 < 11.
Step-by-step explanation:
The correct inequality that can be represented by the number line is option D: 5x - 2 > -22 and 6x - 7 < 11.
To determine the correct answer, we need to understand how to interpret a number line. A point on the number line represents a specific value, while an inequality represents a range of values. The point where two ranges overlap represents the values that satisfy both inequalities.
In option D, the first inequality states that 5x - 2 > -22. Solving this inequality, we get x > -4. The second inequality states that 6x - 7 < 11. Solving this inequality, we get x < 3. The overlapping range between x > -4 and x < 3 represents the values that satisfy both inequalities, which is the correct answer.