Solve and draw a linear inequality
"Solve and draw a linear inequality" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Showing solutions on the number line" in Linear Inequalities. Set a, b, c and the sign. The steps subtract b from both sides and then divide by a. Watch the sign when a is negative, and watch the circle at the end point: hollow for < and >, filled for ≤ and ≥. Adding or subtracting never changes the sign. Dividing by a positive number keeps it; dividing by a negative number reverses it. Hollow circle for strict signs, filled circle for ≤ and ≥. JEE Main asked 2 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Showing solutions on the number line in Linear Inequalities. Change the values and watch what happens.
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
- 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.
Questions
3 answers
- What does the "Solve and draw a linear inequality" simulation show?
- Set a, b, c and the sign. The steps subtract b from both sides and then divide by a. Watch the sign when a is negative, and watch the circle at the end point: hollow for < and >, filled for ≤ and ≥.
- 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 "Showing solutions on the number line" in Linear Inequalities (Class 11 Maths).
Embed this simulation
Free, with a link back
Teaching this idea? Put the simulation on your own page or LMS with this code.