Inequalities
Grades 7–9 Algebra Number line
Real life is full of "at least," "at most," "under," and "over" —
those are inequalities. x > 3 means "any number
bigger than 3" — a whole region, not one answer.
<less than ·>greater than≤less than or equal to ·≥greater than or equal to
Solutions live on a number line
x > −2 — every point right of −2 (open circle: −2 itself is out):
Solving works like equations — with one trap
x + 5 > 9 → x > 4 (subtract 5)
3x ≤ 21 → x ≤ 7 (divide by 3)
−2x < 8 → x > −4 ← sign FLIPS!
The flip rule
Multiply or divide both sides by a negative number
and the inequality sign reverses. Why? −2 < 6, but multiplying by
−1 gives 2 > −6 — the bigger number becomes the smaller one.
Open vs closed dots
>/< → open circle (the edge number is
excluded). ≥/≤ → filled dot (edge included).
Practice
Solve x − 3 > 3 → x > ___
Solve −4x ≥ 20:
Solve 2x + 8 ≤ 4 → x ≤ ___
Next: exponents & powers · Back: two-step equations