Inequalities Worksheets

What it is

An inequality is solved just like an equation (isolate the variable) with one extra rule: multiplying or dividing both sides by a negative flips the direction of the sign.

Why it matters

Inequalities describe ranges of values rather than a single answer, the foundation for graphing solutions, working with constraints, and the reasoning behind functions and calculus.

How to do it

1. Undo addition or subtraction first, then undo multiplication or division.
2. If you multiply or divide by a negative number, flip the inequality sign.
3. Write the solution (e.g., x > 3) and graph it: open circle for < or >, closed for ≤ or ≥, arrow toward the solutions.

Examples by level

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

• Forgetting to flip the inequality sign when multiplying or dividing by a negative.
• Solving it like an equation and losing track of the direction.
• Using an open circle for ≤/≥ (should be closed) or a closed circle for </> (should be open) when graphing.

Tips

• Do the same operation to both sides, exactly like an equation.
• The sign only flips when you multiply or divide by a negative, never for adding or subtracting.

Key vocabulary

inequality

a comparison using <, >, ≤, or ≥

solution set

all the values that make the inequality true

Frequently asked questions

When do you flip the inequality sign?

Only when you multiply or divide both sides by a negative number. Adding, subtracting, or multiplying/dividing by a positive keeps the sign the same.

What do open and closed circles mean on a number line?

An open circle (for < or >) means the boundary value is not included; a closed circle (for ≤ or ≥) means it is included.