SAT Math: Solving Linear Inequalities

The concept, explained

• 1

  Solve inequalities like equations, with one critical exception: when you multiply or divide both sides by a negative number, flip the inequality sign.

• 2

  The solution is a range, written as an inequality (x > 3), interval notation ([3, ∞)), or on a number line.

• 3

  For ≥ and ≤, the endpoint is included (closed circle on a number line). For > and <, it is excluded (open circle).

• 4

  Check by substituting a test value from inside the solution region — it should satisfy the original inequality.

• 5

  When the inequality describes a real-world scenario, check that the solution makes practical sense (e.g., negative quantities of items are impossible).