Simulation · Maths · Class 11

Solve and draw a linear inequality

From the lesson Showing solutions on the number line in Linear Inequalities. Change the values and watch what happens.

The idea behind it

NCERT §5.3

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.

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