Question

Which compound inequality has no solution?

A) Ox>2 and 3x ≤ 9
B) Ox>1 and 2x ≤ 3-2
C) Ox>-1 and 4x ≤ 2-8
D) Ox>-2 and 5x ≤ 2+15

Answer 1

The compound inequality that has no solution is option C) Ox>-1 and 4x ≤ 2-8.

Step-by-step explanation:

The compound inequality that has no solution is option C) Ox>-1 and 4x ≤ 2-8. In order for a compound inequality to have a solution, the intersection of the two inequalities must contain at least one common value of x. Let's analyze option C):

• Ox>-1 means that x is greater than -1.
• 4x ≤ 2-8 simplifies to 4x ≤ -6, which means x is less than or equal to -1.5.

Since x cannot be simultaneously greater than -1 and less than or equal to -1.5, there is no common value of x that satisfies both inequalities. Therefore, option C) has no solution.