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BetterGrades Algebra · Unit A3 · Unit Hub

Unit A3: Inequalities, Absolute Value, and Formulas

Extend algebra from exact equality to ranges, distance conditions, and reusable formulas. How do we describe all values satisfying a condition?

Act III - Describing regions and constraints

The 8-lesson path

Equation methods are adapted to inequalities; negative scaling reveals order reversal; intervals describe regions; absolute value becomes distance; formulas are rearranged without assigning numerical values.

Governing question

How do we describe all values satisfying a condition?

Extend algebra from exact equality to ranges, distance conditions, and reusable formulas.

Mastery design

Know when to continue

Students solve, graph, and interpret mixed inequalities and rearrange formulas with units.

Unit outcomes
  1. Interpret and graph inequality solution sets.
  2. Explain why multiplication or division by a negative reverses order.
  3. Translate among inequality, interval, and number-line forms.
  4. Solve compound and absolute-value inequalities.
  5. Rearrange formulas and preserve units.
Core sequence

Lessons

Move in order when this material is new; use prerequisites and repair links when entering mid-unit.

  1. 01Inequalities and truth setsInterpret an inequality as a condition satisfied by a region of values.
  2. 02Solving linear inequalitiesApply equation-style operations while tracking order and representing the result as a set.
  3. 03Why negative scaling reverses orderExplain order reversal through reflection and numerical comparison.
  4. 04Interval notation and endpoint meaningTranslate among inequalities, number-line graphs, and interval notation.
  5. 05Compound inequalitiesInterpret and solve intersections and unions of conditions.
  6. 06Absolute value as distanceInterpret |x-a| as the distance from a center aa.
  7. 07Absolute-value equations and inequalitiesDerive point, interval, or exterior solutions from distance meaning.
  8. 08Literal equations and formulasIsolate a specified variable while preserving the relationship and units.

Practice around the path

Review, mixed practice, mastery, and investigation

Every route contains a fixed set of concrete questions, with detailed solutions available after an attempt.

ReviewCumulative reviewRevisit this unit with prior-unit retrieval.PracticeMixed practiceClassify the structure before choosing a method.MasteryMastery checkUse the supplied grading and cumulative-share contract.Response guideMastery response guideAttempt-gated rubric support; no invented canonical answers.

Source & rights

Original storyboard, rights-separated references.

Public page content comes from the BetterGrades Algebra editorial storyboard supplied by the owner. Reference books named in provenance remain separate and are not copied into the application.