Integrated_Algebra // Mod_04

INEQUALITIES

Comparing relative values. Moving beyond a single solution to discover the infinite boundaries of truth.

01 // The Region Mapper

Infinite Solutions

An equation ($x = 5$) has exactly one answer. An inequality ($x > 5$) represents an infinite set of numbers. Use the lab below to map out the shaded regions of truth!

Region Mapper

The Statement

x2
True Statement
-10-50510Test: 5

02 // The Logic Gates

>
Greater Than
Open Circle
<
Less Than
Open Circle
At Least
Closed Circle
At Most
Closed Circle

The Golden Rule

You solve inequalities exactly like regular equations with one major exception: When you multiply or divide both sides by a negative number, you must FLIP the inequality symbol!

-2x < 10
Divide by -2
x>-5

04 // Compound Logic

"AND"

Intersection

-2 < x ≤ 5

The solution must satisfy BOTH conditions. It creates a shaded "sandwich" between two boundaries.

"OR"

Union

x < -3 OR x > 4

The solution satisfies EITHER condition. It splits outwards away from the center boundaries.

Practice Arena // Coming Soon

Dynamic Problem Sets

The question engine is offline while we construct the generation architecture. Check back soon for infinite practice problems!

Phase 1 Complete

You have mastered linear realities and boundaries.

Start Phase 2: Quadratics