Inequalities and Regions
Ages 16–18Difficulty adapts to you
Inequalities and Regions
An inequality compares values that may form a range. Adding or subtracting keeps the sign direction; multiplying or dividing by a negative reverses it. For two variables, each inequality describes a half-plane and a system describes an overlapping region.
Your goals
- ✓You can solve inequalities and represent solution sets on number lines and coordinate planes.
- ✓You can use Inequalities and Regions, model correctly.
- ✓You can use the definitions, units, assumptions, and examples to check your answer.
Words to know
- Inequalities and Regions:
- Solve inequalities and represent solution sets on number lines and coordinate planes.
- model:
- A rule or representation used to describe a situation and make a prediction.
Examples
- 1−2x > 6 becomes x < −3 because division by −2 reverses the sign.
- 2Use a solid boundary for ≤ or ≥ and a dashed boundary for < or >.
Check these
- • Do not skip the meaning of a term or give a result without explaining what it means.
- • Keep every number, symbol, label, and unit in its correct place.
- • Show enough working to check how you reached your answer.
Helpful habits
- • Read the whole question before choosing what to do.
- • Show one clear step at a time and check each step.
- • If you are stuck, draw a model, try smaller numbers, or revisit the example.
Now try your own
Create your own inequalities and regions example, solve it, and explain how you checked it.
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Helpful Hints“Look for patterns — maths is full of them!”