Multiplicative Property of Inequality with Whole Numbers

The Multiplicative property of Inequality states that, for any three numbers a, b, and c

If a > b, then ac > bc, if c > 0

If a > b, then ac < bc, if c < 0

A number line can help model what is going on when c > 0, as well as why the inequality sign “flips” when c < 0.

When we multiply, or divide both sides of an inequality by a negative number we change less than into greater than and vice versa or flip the inequality sign.

Solve the following using multiplicative property of inequality −

$\frac{−15}{x}$ > 5

Solution

Step 1:

Given $\frac{−15}{x}$ > 5;

Cross multiplying −15 > 5x

Using multiplicative property of inequality, we divide both sides by 5

−15/5 < 5x/5; −3 < x

Step 2:

So, the solution for the inequality is x > −3

Solve the following using multiplicative property of inequality −

11 ≤ 154 /q

Solution

Step 1:

Given 11 ≤ $\frac{154}{q}$

Cross multiplying 11q ≤ 154

Using multiplicative property of inequality, we divide both sides by 11

$\frac{11q}{11}$ ≤ $\frac{154}{11}$; q ≤ 14

Step 2:

So, the solution for the inequality is q ≤ 14