Linear and simultaneous inequalities

Represent linear-inequality solutions as ranges and find their intersection.

Meaning

A linear inequality has a range of satisfying numbers. A system of inequalities requires the common range satisfying all conditions simultaneously.

Example

Solving and gives and hence It includes 3 but excludes 5.Use the overlap, not the union, of simultaneous conditions. Match endpoint inclusion in inequality notation and on the number line.

Practice for this concept

Scope and references

Topics

Solution ranges, number-line representations, common ranges of several conditions

Learning goal

Represent linear-inequality solutions as ranges and find their intersection.

Helpful background

Check inequality properties and number-line ranges.