Writing and graphing inequalities

This Grade 6 worksheet practices writing and graphing inequalities (Common Core 6.EE.B.8, 6.EE.B.5).

Write an inequality for a situation, and draw solutions on a number line. With an answer key.

On this sheet

• A child under 9 years old gets in free. Let a be the age, in years, of a child who gets in free. Write an inequality that shows this. — answer: a < 9
• A bag can hold no more than 45 kilograms. Let w be the weight in the bag, in kilograms. Write an inequality that shows this. — answer: w ≤ 45
• A soccer team needs at least 14 players. Let p be the number of players. Write an inequality that shows this. — answer: p ≥ 14

How to teach it

1. Undo what was done to the variable, in reverse order: first undo adding or subtracting, then multiplying or dividing.
2. Whatever you do to one side, do to the other, so the equation stays balanced.
3. With brackets, expand first; with the variable on both sides, gather it on one side.
4. With an inequality, multiplying or dividing both sides by a negative number reverses the sign.
5. Check by putting the answer back into the original equation.

Questions teachers ask

How many problems are on this worksheet?

10 on one page, with the answer key on the last page.

What grade and standard is it for?

Grade 6. Common Core: 6.EE.B.8, 6.EE.B.5.

Can I print more than one version?

Yes. Every version has different numbers and its own answer key. Use “Make another version” for a new one; the same version always prints the same.

What grade learns one-step and two-step equations?

In the Common Core, one-step equations are Grade 6 (6.EE.B.7), two-step equations and inequalities are Grade 7 (7.EE.B.4), and multi-step equations with the variable on both sides are Grade 8 (8.EE.C.7).

What is the difference between an equation and an inequality?

An equation says two amounts are equal and usually has one solution. An inequality says one is greater or less than the other, and has a whole range of solutions.