Grade 6 · Algebra & Functions
Inequalities
Learn to describe and solve ranges of possible values through clear explanations, worked examples, an interactive model, and guided practice.
Lesson coverage
Learn the whole topic, not just one problem type.
This lesson and its practice bank deliberately rotate across these core facets so students build a connected understanding of the subject.
Distinguish <, >, ≤, and ≥.
Isolate the variable while preserving the inequality.
Represent solution sets on number lines.
Test whether values belong to a solution set.
Model constraints and ranges in context.
Build the idea
Inequalities is part of the transition into middle-school mathematics through ratios, rational numbers, expressions, equations, geometry, and statistics. Start by identifying what each quantity, symbol, diagram, or graph represents before calculating.
Interpret symbols
Distinguish <, >, ≤, and ≥. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Solve
Isolate the variable while preserving the inequality. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Graph solutions
Represent solution sets on number lines. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Check values
Test whether values belong to a solution set. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Applications
Model constraints and ranges in context. Use a representation that fits the idea, connect it to the relevant mathematical relationship, and explain how the representation supports the result.
Use a reliable strategy
Translate the information into symbols, apply one valid transformation at a time, and check the result in the original relationship.
Check and explain
A correct answer is only part of mathematical understanding. Check units, signs, scale, and whether the result makes sense. Then explain the relationship in words so you can recognize the same structure when the numbers or context change.
Key terms
Words to know
- Inequalities
- The central skill or relationship explored in this lesson.
- Inequality
- A statement comparing quantities that may not be equal.
- Boundary
- A value separating solution and non-solution regions.
- Solution set
- All values that make an inequality true.
Interactive math lab
Change it. See it. Understand it.
Adjust the values and watch the relationship respond.
| Input | 6 |
|---|---|
| Offset | 3 |
| Output | 15 |
Worked examples
See the idea in action.
Subtract 2 from both sides to get x < 6.
Strictly less than excludes the boundary and includes smaller values.
Guided practice
20 questions drawn from a 150-question lesson bank.
Each practice session mixes the major skills in this lesson so you practice the whole topic, not just one repeated problem type.
Which symbol means 'less than or equal to'?
Curriculum reference
Built as a continuous K–12 progression.
The sequence follows widely used K–12 mathematics progressions and references the Common Core mathematics framework. Explanations, examples, interactive models, and practice questions are original FreeLearnHub material.