Question

Which compound inequality has no solution?

Answer 1

Answer: The first option:

x ≤ -2  and 2x ≥ 6

Step-by-step explanation:

A compound inequality will have no solution if the inequalities are contradictory.

An example of this would be:

x > 3 and x < 1

There is no value of x that is at the same time larger than 3, and smaller than 1.

Now, let's analyze the options.

1) x ≤ -2  and 2x ≥ 6

This has no solution, because if x ≥ -2, the maximum value that x can take is x = -2

Replacing that in the other inequality we get:

2*(-2) > 6

-4 > 6

This is false, then this compound inequality has no solution.

2) x ≤ -1  and 5*x < 5

This ineqalty has infinite solutions, one can be x = -2

-2 ≤ -1 and 5*(-2) < 5

are both true.

3) x ≤ -1 and 3x ≥ -3

A solution for this can be x = -1

-1 ≤ -1  is true

3*(-1) ≥ -3

-3 ≥ -3 is true.

Then we have at least one solution here.

4) x ≤ -2  and 4x ≤ -8

Here we have infinite solutions, one can be x = -10

-10 ≤ - 2 is true

4*(-10) ≤ -8

-40 ≤ - 8 is also true.

Then the only option that has no solutions is the first one.