Question

Make up an inequality that has no solution. Make up one that has exactly one solution.

Short answer

The inequality that has no solution is $\sin \left(x\right)>1$ and the inequality that has exactly one solution is $x^2\le 0$.

Step-by-step solution

Given information

The inequality which has no solution and another inequality which has exactly one solution.

Determine the inequality

Since, the value of sine function does not exceed 1 , the inequality with no solutions can be:

$\sin \left(x\right)>1$

Since square of an expression cannot be less than 0 ,

$x^2\ge 0$

To get only one solution, the inequality can be modified as:

$x^2\le 0$

Write the conclusion

The inequality which has no solution is $\sin \left(x\right)>1$.

The inequality which has exactly one solution is$x^2\le 0$