Question

Which compound inequality has no solution?

Option 1: x > 2 and 3x ≤ 9
Option 2: x > 1 and 2x ≤ –2
Option 3: x > –1 and 4x ≥ –8
Option 4: x > –2 and 5x ≥ 15

Answer 1

Option 4: x > –2 and 5x ≥ 15 is the compound inequality that has no solution.

Step-by-step explanation:

To determine which compound inequality has no solution, we need to solve each one of them individually. Let's break it down:

1. Option 1: x > 2 and 3x ≤ 9
   Simplifying the second inequality, we have x ≤ 3. Therefore, the compound inequality is x > 2 and x ≤ 3. This compound inequality has a solution because there are values of x that satisfy both conditions.
2. Option 2: x > 1 and 2x ≤ –2
   Simplifying the second inequality, we have x ≤ –1. Therefore, the compound inequality is x > 1 and x ≤ –1. This compound inequality has no solution because there are no values of x that satisfy both conditions simultaneously.
3. Option 3: x > –1 and 4x ≥ –8
   Simplifying the second inequality, we have x ≥ –2. Therefore, the compound inequality is x > –1 and x ≥ –2. This compound inequality has a solution because there are values of x that satisfy both conditions.
4. Option 4: x > –2 and 5x ≥ 15
   Simplifying the second inequality, we have x ≥ 3. Therefore, the compound inequality is x > –2 and x ≥ 3. This compound inequality has no solution because there are no values of x that satisfy both conditions simultaneously.

So, the compound inequality that has no solution is Option 4: x > –2 and 5x ≥ 15.