Numbers on a number line
Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations
What a learner can do afterwards
- Write an inequality from a worded constraint (e.g., 'must be at least 12' → x ≥ 12)
- Represent the solution set of an inequality on a number line with open or closed circles
- Solve a one-step or two-step inequality such as 3x + 1 < 10
The lesson
You already know how to solve an equation like x + 3 = 10, where both sides end up exactly equal. An inequality compares two expressions without an equal sign. It uses one of four symbols: < (less than), > (greater than), ≤ (less than or equal to, or 'at most'), and ≥ (greater than or equal to, or 'at least').
A club rule says, 'You must be at least 12 to join.' If x stands for your age, that rule becomes x ≥ 12. The words 'at least' turn into ≥, because 12 works and so does any age above it.
Solve 3x + 1 < 10 the same way you'd solve an equation: undo the operations in reverse order. Subtract 1 from both sides: 3x < 9. Divide both sides by 3: x < 3. Every number smaller than 3 makes the inequality true.
An equation usually has one exact answer. An inequality has a whole set of answers on one side of a boundary number. A closed circle on the number line means the boundary counts as a solution; an open circle means it doesn't.
An inequality compares expressions with <, >, ≤, or ≥; solve it the same way you solve equations, then show the answer as a range on a number line with an open or closed circle.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.