Inequalities (introduction)
<, >, ≤, ≥. Solve like equations — but flip the sign when multiplying or dividing by a negative.
Inequalities allow ranges of solutions: x > 3 means ‘x is more than 3’. Solving uses the same balance method as equations, with one critical exception: multiplying or dividing both sides by a negative reverses the inequality.
Worked examples
x + 4 > 9 ⇒ x > 5.
3x ≤ 12 ⇒ x ≤ 4.
−2x < 8 ⇒ x > −4. Flipped because we divided by −2.
Frequently asked questions
Number line how?
Open circle for < or > (not included); filled circle for ≤ or ≥ (included). Arrow shows direction of solutions.
Why flip when dividing by a negative?
Because order reverses. 3 > 2, but −3 < −2.