Q3. - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

Step 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Meaning of &ldquo;Inequality with solution set as empty set&rdquo;

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

Step 3 - 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

$\begin{array}{c}0<0\left(\text{False}\right)\\ 4x+2<4x+2\left(\text{Add same number}\right)\\ \frac{4x+2}{6}<\frac{2\left(2x+1\right)}{6}\left(\text{Divide by positive number}\right)\\ \frac{4x+2}{6}<\frac{2x+1}{3}\end{array}$

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