Question

For which values of a the system has no solution: x≤5, x≥a

Answer 1

Given:

The system of inequalities is

$x\leq 5$

$x\geq a$

To find:

The values of a for which the system has no solution.

Solution:

We have,

$x\leq 5$        ...(1)

It means the value of x is less than or equal to 5.

$x\geq a$        ...(2)

It means the value of x is greater than or equal to a

Using (1) and (2), we get

$a\leq x\leq 5$

But if a is great than 5, then there is no value of which satisfies this inequality.

Therefore, the system has no solution for a>5.