Simulation · Maths · Class 11

Where two conditions overlap

From the lesson Systems of inequalities in one variable in Linear Inequalities. Change the values and watch what happens.

The idea behind it

NCERT §5.3

A system asks for values of x that satisfy two or more inequalities together. Solve each one, then take the values common to all, which is the intersection of the solution sets.
Worked example: 2x − 3 < x + 4 and 3 − 2x ≤ −1. The first gives x < 7. The second gives −2x ≤ −4, so x ≥ 2. Together: 2 ≤ x < 7, that is, [2, 7).
On the number line, shade each solution set on its own line and keep only the stretch shaded on both. The ends keep their own circle types, filled at 2 and hollow at 7.
A system can have no solution. x + 2 > 7 gives x > 5 and 2x < 4 gives x < 2; no number is both above 5 and below 2, so the solution set is empty, ∅.
A system can also collapse to one point: x ≥ 3 and x ≤ 3 together give only x = 3.
A double inequality is a system in short form: 1 ≤ x < 6 is the same as x ≥ 1 and x < 6.

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