Mathematics · Class 11 Science
Ch 5Linear Inequalities — Class 11 Mathematics, concept-first.
A statement involving the symbols is called an inequality (or an inequation). Just as an equation asserts that two expressions are equal, an inequality asserts that one expression is less than, greater than, less than or equal to, or greater than or equal to another.
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Algebraic Solution of Linear Inequalities in One Variable
Solving a linear inequality algebraically isolates the variable using the same style of operations as solving an equation, with one crucial difference: adding or subtracting any quantity, or multiplying or dividing by a…
Most relevant Q&A
- The marks obtained by a student in two tests are 65 and $x$. Find the range of values of $x$ so that the average of the two marks is at leas…Free
- Solve $-\dfrac{x}{3} + 2 > 5$ for real $x$, showing every step; represent the solution on the number line.Free
- Solve the compound inequality $-5 \le \dfrac{3x+2}{4} < 4$ for real $x$, and write the solution as an interval.Preview
- Solve $\dfrac{3(x-2)}{5} \ge \dfrac{5(2-x)}{3}$ for real $x$.Free
- Solve $10 - 4x > 2$ for real $x$, being careful with the sign when dividing.Preview
In previous exams
How often this chapter’s concepts have been examined — real appearance data, never estimated.
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction to Inequalities
A statement involving the symbols is called an inequality (or an inequation). Just as an equation asserts that two expressions are equal, an inequality asserts that one expression is less than, greate…
Algebraic Solutions of Linear Inequalities in One Variable
Solving a linear inequality algebraically means performing a sequence of legal operations on both sides until the variable stands alone, exactly as with an equation — but two of the rules behave diffe…
Inequalities Involving the Modulus Function
The modulus (or absolute value) of a real number , written , is defined piecewise as Geometrically, is the distance of the point from the origin on the number line, always non-negative: for every real…
Representation on the Number Line
Once the solution set of a one-variable linear inequality has been found algebraically, it can be pictured directly on the number line — a single horizontal line marked with the real numbers in increa…
Graphical Solution of Linear Inequalities in Two Variables
A linear inequality in two variables, such as , is satisfied not by isolated points on a line but by an entire region of the Cartesian plane — because for almost every value of , a whole range of -val…
Summary
This chapter developed the algebra and geometry of linear inequalities, extending the equation-solving skills built earlier in the course.
Sample & Board Papers
Sample papers and previous-year board questions for this subject.
+−Show 1 questionHide questions1 question
More questions
23 Q+−Show 2 questionsHide questions2 questions
+−Show 6 questionsHide questions6 questions
- Example 1Solve the inequality $3x - 5 < 7$ for real $x$, and represent the solution set on the number line.Free
- Example 2Solve $-\dfrac{x}{3} + 2 > 5$ for real $x$, showing every step; represent the solution on the number line.Free
- Example 3Solve the compound inequality $-5 \le \dfrac{3x+2}{4} < 4$ for real $x$, and write the solution as an interval.Preview
- Example 4Solve the modulus inequality $|x - 3| < 4$ for real $x$, and represent the solution on the number line.Preview
- Example 5Solve $|2x + 1| \ge 5$ for real $x$, and write the solution set using interval notation.Preview
- Example 6Solve graphically: $3x - 2y \ge 6$. State whether the boundary line is drawn solid or dashed, and identify which half-plane is the solution…Preview
+−Show 4 questionsHide questions4 questions
- Q7Solve $7x - 3 \le 5x + 11$ for real $x$.Free
- Q8Solve $\dfrac{3(x-2)}{5} \ge \dfrac{5(2-x)}{3}$ for real $x$.Free
- Q9Solve $10 - 4x > 2$ for real $x$, being careful with the sign when dividing.Preview
- Q10Solve the compound inequality $-1 \le 2x + 5 < 9$ for $x$ an integer, and list the solution set.Preview
+−Show 4 questionsHide questions4 questions
+−Show 3 questionsHide questions3 questions
- Q15Represent the solution set of $2x - 1 > 5$ (real $x$) on the number line, and state whether the boundary point is included.Free
- Q16Represent the solution set $-3 \le x < 4$ on the number line, describing the type of circle used at each end.Preview
- Q17The solution of $|x| \le 5$ is to be shown on the number line as a shaded segment with circles at both ends. Find the two endpoints and stat…Preview
+−Show 4 questionsHide questions4 questions
- Q18Solve graphically: $x + y < 5$. State the type of boundary line and shade the solution region, using the origin as a test point.Free
- Q19Solve graphically: $4x + 3y \le 12$. State the type of boundary line and identify the solution half-plane.Free
- Q20Solve the system $x \ge 0$, $y \ge 0$, $2x + y \le 10$ graphically, and find the coordinates of the vertices of the bounded solution region.Preview
- Q21Solve the system $y > 2x - 3$ and $y \le -x + 4$ graphically. State which boundary line is solid, which is dashed, and describe the directio…Preview