Lesson 7: Solve Inequalities

Property

On a number line, numbers increase in value from left to right. We use inequality symbols to show ordering:

• $a < b$ (read $a$ is less than $b$) when $a$ is to the left of $b$.
• $a > b$ (read $a$ is greater than $b$) when $a$ is to the right of $b$.

Examples

• To compare 15 and 8, we see 15 is to the right of 8 on the number line, so $15 > 8$.

Property

When graphing inequalities on a number line, we use different symbols to show whether the boundary point is included in the solution set.
For strict inequalities like $x > 3$ or $x < 3$, we use an open circle at the boundary point to show it is not included.
For non-strict inequalities like $x \geq 3$ or $x \leq 3$, we use a closed circle (or filled dot) at the boundary point to show it is included.
We then shade the number line in the direction that contains all the solutions.

Examples

Property

A solution of an inequality is any value that makes the inequality true when substituted. The solution set is the collection of all solutions, which for linear inequalities contains infinitely many values.

Examples