Solving Equations and Inequalities
Linear equations: Isolate the variable using inverse operations. Whatever you do to one side, do to the other.
Inequalities: Same rules as equations, except multiplying or dividing both sides by a negative number flips the inequality sign. −2x < 6 → x > −3.
Systems of equations: - Substitution: Solve one equation for one variable, substitute into the other. - Elimination: Add/subtract equations to cancel one variable.
Quadratic equations (ax² + bx + c = 0): - Factor and set each factor = 0. - Quadratic formula: x = [−b ± √(b² − 4ac)] / (2a) - Discriminant (b² − 4ac): > 0 → two real solutions; = 0 → one; < 0 → no real solutions.