Unit 04 · Family Guide

The World of Constraints

Help the learner reason about allowed values, boundaries, and distance—not merely flip symbols by memory.

Unit Home

Useful prompts

  • What values are allowed?
  • Is the boundary included?
  • Which direction should the solution extend?
  • Did you multiply or divide by a negative?
  • Is this an AND intersection or OR union?
  • What distance does the absolute value describe?

Misconceptions to watch

  • Using brackets with infinity.
  • Confusing shading direction.
  • Reversing the sign because a negative merely appears.
  • Forgetting reversal after negative scaling.
  • Confusing AND with OR.
  • Solving only one branch of an absolute-value equation.
  • Reading |x−a|>k as an inside interval instead of outside regions.

Evidence to preserve

One corrected boundary error, one sign-reversal explanation, pathway practice, Constraint Design Lab, Boss Battle, and mastery result.