Question

Select the correct answer.

Which inequality can this number line represent?




A.

x + 5 > 8 or 3 + 2x < -5

B.

x + 5 > 8 and 3 + 2x < -5

C.

5x − 2 > -22 or 6x − 7 < 11

D.

5x − 2 > -22 and 6x − 7 < 11

Answer 1

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.