Math · Algebra · H.E.

Linear inequalities in one or two variables

Linear inequalities punish the one algebraic habit everyone forgets under time: flip the sign when you multiply or divide by a negative.

What Bluebook is testing

H.E. is one- or two-variable inequalities, compound AND/OR, and graphs of half-planes. Hard items ask which k makes every real x a solution — or none.

How it shows up

Number-line graphs, shaded regions, and 'which of the following is equivalent.' The identity-style items from H.A. come back with an inequality.

A method that survives Module 2

Isolate, then test one number from your solution set in the original inequality. For 'every real is a solution,' the inequality must collapse to a true statement with no x. On a graph, pick a test point (0, 0) unless it sits on the line.

Traps that look like knowledge

  • Not flipping the inequality when multiplying by a negative
  • Treating a compound AND as OR (overlap vs union)
  • Shading the wrong side of a two-variable inequality
  • Picking a boundary value that does not satisfy a strict inequality

Questions

What is "Linear inequalities in one or two variables" on the Digital SAT?
It is an official College Board skill in Digital SAT Math. The wording on Bluebook matches the domain taxonomy Drilled uses in drills, analytics, and the notebook.
How does Drilled train Linear inequalities in one or two variables?
Filter the bank to the skill, run a timed drill, autopsy every miss, and let the notebook bring the same pattern back. Domain drills and full section sims include the skill at the official mix.
What is the most common trap on Linear inequalities in one or two variables?
Not flipping the inequality when multiplying by a negative

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