Linear Inequalities

Maths · Class 11

Simulation · Maths · Class 11

Where two conditions overlap

"Where two conditions overlap" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Systems of inequalities in one variable" in Linear Inequalities. Set two conditions on x. Each gets its own number line; the bottom line keeps only the values that pass both, which is the solution of the system. The solution of a system is the intersection of the separate solution sets. Each end keeps its own circle type, and the intersection can be a stretch, a single point or empty. JEE Main asked 2 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).

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

Where two conditions overlapMaths · Class 11

In JEE Main

42 shifts analysed

2 questions from Linear Inequalities across the 42 JEE Main shifts Lumi has analysed (2017–2026).

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.

Questions

3 answers

What does the "Where two conditions overlap" simulation show?
Set two conditions on x. Each gets its own number line; the bottom line keeps only the values that pass both, which is the solution of the system.
Does JEE Main ask questions from Linear Inequalities?
Yes. JEE Main asked 2 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
Is this simulation free?
Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Systems of inequalities in one variable" in Linear Inequalities (Class 11 Maths).

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