Question

Write an inequality for which solution set is the empty set.

Short answer

Inequality for which solution set is an empty set is $\frac{4x+2}{6}<\frac{2x+1}{3}$

Step-by-step solution

- Write properties of inequality

Properties of inequalities are written in following table:

- Meaning of “Inequality with solution set as empty set”

Solution of an inequality is empty set when on solving it a universal false statement is obtained

- Write an inequality whose solution is empty set

To write such example take one wrong statement and then use properties of inequalities as shown below

$\begin{array}{c}0<0\left(\text{False}\right)\\ 4x+2<4x+2\left(\text{Addsamenumber}\right)\\ \frac{4x+2}{6}<\frac{2\left(2x+1\right)}{6}\left(\text{Dividebypositivenumber}\right)\\ \frac{4x+2}{6}<\frac{2x+1}{3}\end{array}$

Thus, required inequality is $\frac{4x+2}{6}<\frac{2x+1}{3}$