- Writing, Graphing and Solving Inequalities
- Home
- Translating a Sentence by Using an Inequality Symbol
- Translating a Sentence into a One-Step Inequality
- Introduction to Identifying Solutions to an Inequality
- Writing an Inequality for a Real-World Situation
- Graphing a Linear Inequality on the Number Line
- Writing an Inequality Given a Graph on the Number Line
- Identifying Solutions to a One-Step Linear Inequality
- Additive Property of Inequality with Whole Numbers
- Multiplicative Property of Inequality with Whole Numbers
- Solving a Two-Step Linear Inequality with Whole Numbers
- Solving a Word Problem Using a One-Step Linear Inequality

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
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# 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