The same moves as an equation, with one exception: multiplying or dividing by a negative flips the sign round.
| Symbol | Reads as | On the number line |
|---|---|---|
| x > 3 | x is greater than 3 | Open circle at 3, arrow right |
| x < 3 | x is less than 3 | Open circle at 3, arrow left |
| x ≥ 3 | x is greater than or equal to 3 | Filled circle at 3, arrow right |
| x ≤ 3 | x is less than or equal to 3 | Filled circle at 3, arrow left |
3x + 5 = 20 gives one value. 3x + 5 > 20 gives every value above 5, which is infinitely many.
The open and filled circle
An open circle means the number itself is not included; a filled one means it is. That small mark carries real information.
3 < 5 is true. Multiply both sides by −1 and you get −3 and −5, but −3 is GREATER than −5, so the sign must turn round.
Subtracting 5 from both sides leaves the sign exactly as it was. Sliding both numbers along the line does not change which is further right.
Avoiding the flip altogether
Move the negative x term instead of dividing by a negative. 10 − 2x > 4 becomes 10 > 4 + 2x, giving x < 3 with no flip needed.
Try a value your answer allows, then a value it excludes. Both tests together confirm the direction of the sign.
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