Skill: systems-inequalities

Inequalities Practice

An endless supply of never-repeating inequalities problems: test points, choose the shaded side, pick solid or dashed, find feasible points and vertices, and read shaded graphs.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Problem

How to enter answers

Yes/no: type yes or no.
Side/boundary: type above / below / solid / dashed.
Points: type (2, 1) — parentheses optional.
Graph choice: pick the matching inequality.

2 What you’ll practice

Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.

Decide

Test points and choose shading side and boundary style.

y ≥ 2x+1, (1,4) → yes

Find points

Pick a point in the feasible region; locate the vertex.

overlap of shadings → (2, 1)

Read graphs

Match a shaded half-plane to its inequality.

shaded above, dashed → y > 2x+1

3 Watch out for these

The mistakes students make most often on these problems.

1. Wrong side

Wrong: shading below for y > 2x + 1. Right: the sign points the way — above.

2. Swapped boundary

Wrong: dashed for y ≤ x. Right: ≤/≥ → solid.

3. One side only

Wrong: circling one inequality’s side. Right: the system needs the overlap.

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