Solving Inequalities

Solve inequalities almost exactly like equations. For 3x - 7 > 14: add 7 to get 3x > 21, divide by 3 to get x > 7. One critical exception: when you multiply or divide by a negative number, the inequality flips direction. So -2x < 10 becomes x > -5 after dividing by -2.

Why does the sign flip? Consider -2 × 3 = -6 and -2 × 5 = -10. Larger input (5) gives a smaller output (-10) because negation reverses order. The flip rule protects the truth of the statement when negation turns the number line upside down.