- 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

# Translating a Sentence by Using an Inequality Symbol

Inequality is a statement that two quantities are not equal.

These are the following inequality signs for any two quantities A, B

<, A < B; A is less than B

≥, A ≤ B, A is less than or equal to B

>, A > B; A is greater than B

≥, A ≥ B, A greater than or equal to B

≠, A ≠ B; A not equal to B

### Definition

Equations and inequalities are both mathematical sentences that relate two expressions to each other.

In an inequality, the two expressions are related by the symbols: >, <, ≤ or ≥

An equation or an inequality that contains at least one variable is called an open sentence.

When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.

Write an inequality for the following statement

4 greater than or equal to p

### Solution

**Step 1:**

We start from the left and proceed towards the right

On the left, there is 4 and on the right, there is ‘p’ and the inequality ‘greater than or equal to’ in the middle

**Step 2:**

So the statement “4 greater than or equal to p” translates to

4 ≥ p

Write an inequality for the following statement

y less than or equal to 6

### Solution

**Step 1:**

We start from the left and proceed towards the right

On the left, there is y and on the right, there is ‘6’ and the inequality ‘less than or equal to’ in the middle

**Step 2:**

So, the statement “y less than or equal to 6” translates to

y ≤ 6