Lesson 1: Writing and Graphing Inequalities

Property

An inequality is used in algebra to compare two quantities that may have different values. We use inequality symbols to show these relationships:
$a < b$ is read $a$ is less than $b$
$a > b$ is read $a$ is greater than $b$
$a \leq b$ is read $a$ is less than or equal to $b$
$a \geq b$ is read $a$ is greater than or equal to $b$

Examples

Property

To translate English sentences into inequalities, we need to recognize the phrases that indicate the inequality. Some common phrases are 'is greater than' ($>$), 'is at least' ($\geq$), 'is less than' ($<$), and 'is at most' ($\leq$).

Examples

• 'Thirty less than a number $n$ is at least 50' translates to $n - 30 \geq 50$.
• 'Four times a number $y$ is no more than 24' translates to $4y \leq 24$.
• 'A number $p$ increased by 10 exceeds 25' translates to $p + 10 > 25$.

Explanation

Math has its own language. Learning keywords helps you translate from English to an inequality. 'Exceeds' means 'greater than,' while 'at most' means 'less than or equal to.' Pay close attention to these phrases.