Skill: Write and solve simple inequalities

An inequality compares two amounts. The symbols mean:

• $<$ means “less than”
• $>$ means “greater than”
• $\leq$ means “less than or equal to”
• $\geq$ means “greater than or equal to”

Example

A number plus 3 is less than 10. What numbers could the number be?

Step 1: Choose a variable

Let $x$ represent the number.

Step 2: Write the inequality

“Plus 3” means add $3$, and “is less than 10” means use $<10$:

$$x+3<10$$

Step 3: Undo the addition

Subtract $3$ from both sides:

$$x+3-3<10-3$$

So,

$$x<7$$

Step 4: Describe the solution

The answer is every number less than 7. For example, $6$, $0$, and $-2$ all work.

On a number line, use an open circle at $7$ because $7$ is not included, and shade to the left:

$$\leftarrow\!\!-\!\!-\!\!-\!\!-\!\!\circ\; \longrightarrow \qquad\quad 7$$

The solution is:

$$\boxed{x<7}$$