Showing solutions on the number line

The solution set of a linear inequality in one variable is drawn on a number line as a shaded ray or segment.

For x < a or x > a, draw an open (hollow) circle at a, since a is not a solution, and shade to the left or to the right.

For x ≤ a or x ≥ a, draw a filled (dark) circle at a, since a is a solution, and shade to the left or to the right.

Interval notation says the same thing in symbols: x < 4 is (−∞, 4), x ≥ 2 is [2, ∞), 1 ≤ x < 6 is [1, 6), and −1 < x < 3 is (−1, 3). A round bracket excludes the end; a square bracket includes it.

∞ and −∞ are not numbers, so they always take round brackets.

Example: 3x + 1 ≥ 7 gives x ≥ 2, drawn as a filled circle at 2 with the line shaded to the right, or [2, ∞).

When x must be an integer, the picture is a row of dots rather than a shaded line: x < 4 over the integers is the dots …, 1, 2, 3.