Skill: Interpret inequality symbols in context

Inequality symbols compare two quantities:

• $<$ means less than
• $>$ means greater than
• $\le$ means less than or equal to
• $\ge$ means greater than or equal to

The line underneath $\le$ or $\ge$ means the boundary value is allowed.

Example: A school backpack may weigh no more than 10 kilograms. What inequality describes the possible backpack weights?

Step 1: Choose a variable.
Let $w$ be the backpack’s weight in kilograms.

Step 2: Understand the words.
“No more than 10” means the weight can be 10 or less. The backpack may weigh exactly $(10)$ kilograms, so the boundary is included.

Step 3: Write the inequality.

$$w \le 10$$

This means the backpack can weigh $(10)$ kilograms or any amount less than $(10)$ kilograms. For example, $8$, $(9.5)$, and $(10)$ satisfy the inequality, but $(10.1)$ does not.

On a number line, use a closed dot at $(10)$ because $(10)$ is included, and shade to the left because the weights are less than $(10)$.