Math practice · reimagined
Inequalities Game
In this inequality game, x is multiplied by 2 to 6 and kept under a limit, as in 5x < 27, and the answer is a whole number from 2 to 15. Reach that edge before your rival, and your fighter swings first.
Ages 4–99+ · no download · plays in your browser · 23 languages
What is an inequality in math?
An inequality is a math sentence saying that one amount is smaller or bigger than another, written with < (less than) or > (greater than). When it holds a letter, many numbers can make it true. Picture a shelf that holds less than 20 kg: 3 boxes of 5 kg fit, but 4 boxes weigh exactly 20 kg, so they do not.
Every level of Inequalities
Example: the largest whole x in 3x < 40
- The question wants the biggest whole number x for which 3 times x stays under 40.
- Count how many threes fit into 40: thirteen of them make 39, with 1 left over.
- Fourteen threes would make 42, which is past 40, so 14 is too big.
- The largest whole x is 13, so you type 13.
Learn it step by step
An equation asks which number makes both sides equal. An inequality asks which numbers make one side SMALLER than the other — and usually there are infinitely many of them.
You solve it exactly like an equation: to get x on its own in 6x < 47, divide both sides by 6, giving x < 7.83…
So every number below 7.83 works — 7 works, 6 works, 0 works, −100 works. But there is a largest WHOLE number that works, and that is 7. Eight is already too big, because 6 × 8 = 48, which is past 47.
A good way to check: multiply your answer back by the coefficient and make sure it lands under the limit, then check that one more would overshoot.
One warning for later: if you ever divide an inequality by a NEGATIVE number, the sign flips direction. That does not happen here, but it is the rule that catches everyone.
Divide, then type the largest whole number that still fits.
Tips and common mistakes
- Think of the number after < as a ceiling that x can never touch. In 4x < 30, 4 × 7 = 28 stays under it, while 4 × 8 = 32 breaks through.
- Rounding up is a common slip. In 2x < 19, x must stay under nine and a half, and 2 × 10 = 20 is too big, so the answer is 9.
- Pour out 23 dried beans and have your child make piles of 4. Five full piles leave 3 over, so 5 is the largest whole x in 4x < 23.
How to play
Every round shows one inequality, such as 6x < 34, with “largest whole x=?” underneath, and the number in front of x never divides the limit exactly. Type that largest x on the keypad, here 5, since 6 × 6 = 36 is already too much. Enter it first and Garlic strikes, and your speed sets the damage.
— Quick answers —
Inequalities: the short FAQ
- What does x < 5 mean?
- The inequality x < 5 says that x is a number smaller than 5, without saying which one. Many numbers fit: whole ones such as 4 or 0, negative ones such as −3, and halves such as four and a half. The number 5 itself does not fit, because 5 is not less than 5. Among the whole numbers, the largest that fits is 4.
- How do you solve a two-step inequality?
- You solve a two-step inequality much like an equation, by undoing each step on both sides. For 2x + 3 < 15, take 3 from both sides to get 2x < 12. Then halve both sides to get x < 6. Every number under 6 works, so the largest whole number that works is 5, and 2 × 5 + 3 = 13 confirms it.
- How do you remember when to flip the inequality sign?
- The sign flips only when you multiply or divide both sides by a negative number, and a quick test with real numbers proves it. Start from 2 < 5, which is true. Multiply both sides by −1 and you get −2 and −5, but now −2 is the bigger number, so the sign must turn: −2 > −5. Adding or subtracting never flips it, and neither does multiplying or dividing by a positive number.
- Why does my child get inequality word problems wrong?
- Word problems hide the sign inside everyday words, and children often pick the wrong one. “Less than” and “fewer than” become < in math, while “at most” and “no more than” let the limit itself count, written ≤. Ask your child to underline the limit words before writing anything. A box that must hold fewer than 20 books, packed in stacks of 3, gives 3x < 20: at most 6 stacks.
- Can teachers run this linear inequality game in class at no cost?
- They can: the one level is free in any school browser, and pupils play without logins or downloads. For solving inequalities practice, draw a number line from 0 to 10 and write 3x < 25. Pupils take turns circling each whole number that works, checking it by multiplying. The circles stop at 8, since 3 × 9 = 27 overshoots. The schools plan, priced per student, adds a teacher dashboard that tracks who is getting faster.