Skip to content
← Mathematics and Statistics

Mathematics and Statistics · Class 11 Commerce

Ch 17Linear Inequations — Class 11 Mathematics and Statistics, concept-first.

This Maharashtra Std XI (Commerce) Mathematics and Statistics chapter studies linear inequations — statements that compare two expressions using an inequality sign rather than an equals sign.

13

Q&A

3

Concepts

Not available

Exam weightage

Start learning — read this chapter →

Key concepts

Hover a concept to preview it and jump to its most relevant Q&A.

Linear Inequations in One Variable

A linear inequation in one variable, with , is solved like a linear equation with one extra rule: multiplying or dividing both sides by a negative number reverses the inequality sign (, ).

Most relevant Q&A

Start with this concept →

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Inequations and the Rules for Solving Them

This Maharashtra Std XI (Commerce) Mathematics and Statistics chapter studies linear inequations — statements that compare two expressions using an inequality sign rather than an equals sign.

2

Linear Inequations in One Variable — Solution and the Number Line

A linear inequation in one variable has the form (or with ), where and are real. Its solution is always an interval — a ray of the real line — which we both state in interval form and draw on a number…

3

Linear Inequations in Two Variables — Graphical Solution (Half-Planes)

A linear inequation in two variables has the form (or with ), where are not both zero. Its solution is not a set of isolated points but an entire region of the coordinate plane — a half-plane.

4

Systems of Linear Inequations and the Feasible Region

In real problems several conditions must hold at the same time — a factory's labour hours and its material and the non-negativity of quantities.

Exercises

+Show 4 questions4 questions
  1. Q6The solution of the inequation $-2x>6$ over $\mathbb{R}$ is: (A) $x>-3$ (B) $x<-3$ (C) $x>3$ (D) $x<3$Free
  2. Q9Draw the graphical solution of $x\ge 2$ in the coordinate plane.Free
  3. Q12For the inequation $x+y\le 5$, the half-plane that forms its solution: (A) contains the origin and includes the line (B) contains the origin…Preview
  4. Q13A trader has at most ₹12{,}000 to invest and buys two items: item A costing ₹300 each and item B costing ₹200 each. If $x$ and $y$ are the n…Preview

More questions

+Show 9 questions9 questions
  1. Example 1Solve the inequation $3x-5<7$ for $x\in\mathbb{R}$ and represent the solution on the number line.Free
  2. Example 2Solve $2x+3\ge 5x-6$ for $x\in\mathbb{R}$.Free
  3. Example 3Solve the combined inequation $-3<2x+1\le 5$ for $x\in\mathbb{R}$ and write the solution in interval form.Free
  4. Example 4Solve $\dfrac{2x-1}{3}\le \dfrac{x+2}{2}$ for $x\in\mathbb{R}$.Preview
  5. Example 5Solve $5-2x\ge 1$ where $x$ is a natural number, and list the solution set.Preview
  6. Example 7Show the graphical solution of the inequation $2x+3y\le 6$ in the coordinate plane.Preview
  7. Example 8Represent the solution set of $x-2y>4$ graphically.Preview
  8. Example 10Find and shade the feasible region of the system $x+y\le 4,\ x\ge 0,\ y\ge 0$.Preview
  9. Example 11Determine the feasible region of the system $2x+y\le 8,\ x+2y\le 10,\ x\ge 0,\ y\ge 0$ and list its corner points.Preview