Meet the crocodile symbols, draw circles and arrows on a number line, and solve little puzzles. Play, solve missions, crack puzzles and beat the clock.
Start here. An inequality compares two numbers that are not the same. There are four symbols. < means "is less than". > means "is greater than". ≤ means "is less than or equal to". ≥ means "is greater than or equal to". Think of a crocodile: its mouth always opens toward the bigger number, so 3 < 7 and 7 > 3 say the same thing.
On a number line. The inequality x > 4 says x can be any number bigger than 4: 5, 6, 7 and on and on. We draw a circle at 4 and an arrow that keeps going. An open circle means the number itself is not included. A closed circle means it is included. So x > 4 has an open circle at 4, and x ≥ 4 has a closed circle at 4.
Solving. Solve an inequality like an equation: do the same thing to both sides. For x + 2 > 7, take 2 from both sides to get x > 5. For 3x ≤ 12, divide both sides by 3 to get x ≤ 4. For two steps, such as 2x + 1 < 9, take away 1 first (2x < 8) and then divide by 2 (x < 4).
Between two numbers. The inequality 3 < x ≤ 7 means x is bigger than 3 and at most 7. The whole numbers that fit are 4, 5, 6 and 7, so there are 4 of them. Draw it with an open circle at 3, a closed circle at 7 and a line in between.
Words to symbols. "At most 8" is ≤ 8. "At least 5" is ≥ 5. "More than 12" is > 12. "Fewer than 20" is < 20. Later in school you will learn that multiplying or dividing by a negative number flips the symbol. This game only uses positive numbers, so you will not need that yet.
Try this above. In Play, pick a symbol and change the number and watch the glowing numbers. Then switch the circle from open to closed. At the top level, drag the two ends to count the numbers in between, and use the solver to see each step.
An inequality is a sentence that compares numbers with a symbol such as <, >, ≤ or ≥, instead of saying they are exactly equal. For example, x > 4 means x is any number bigger than 4.
An open circle means the number at the circle is not part of the answer. A closed (filled) circle means it is. On the line for x > 4 the circle at 4 is open, because 4 is not bigger than 4.
It means "less than or equal to". The number can be smaller than the one next to the symbol, or exactly that number. So x ≤ 6 fits 0, 1, 2, 3, 4, 5 and 6.
For whole numbers, the first whole number bigger than 4 is 5. So both fit 5, 6, 7 and so on. The pictures are different, with a closed circle at 5 and an open circle at 4, but they pick out the same whole numbers. In the building tasks, either picture is accepted.
Just starting: the four symbols and which numbers fit. I know the basics: drawing and reading number lines and one-step solving. Challenge me: between two numbers, two-step solving and word problems.
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