Linear Inequalities
An inequality's solution isn't one number — it's a whole range, or in two variables, a whole shaded region. Choose an operator and drag the boundary to see how the solution set shifts.
Inequalities solve almost exactly like equations — isolate the variable using the same steps. The one rule that trips people up: multiplying or dividing both sides by a negative number flips the inequality sign.
On a number line, a closed (filled) circle means the boundary value is included (≤ or ≥); an open circle means it’s excluded (< or >). The shaded direction shows every value that makes the inequality true.
The SAT tests this three ways: solving an inequality algebraically, reading a solution off a number line, and reading a solution region off an xy-graph — so it’s worth being comfortable translating between the symbol and the picture in every direction.