5. Linear Inequalities

5 topics1 h

Chapter 5 of NCERT Mathematics for Class 11: Linear Inequalities. Two sections — When a situation refuses to become an equation and Solving one in a single variable. Five videos, 1 h in all.

Worked answers to the 40 exercise questions in this chapter: Exercise 5.1 · Miscellaneous Exercise

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Part 1

When a situation refuses to become an equation

12 minEveryday constraints that fix a range rather than a valueSam has two hundred coins and rice sold only in packets of thirty. Six packets leave twenty coins unspent; seven cost more than the purse holds — the boundary is never hit.12 min · 12 parts

13 minSorting inequalities: numerical or literal, strict or slack, linear or notTen inequalities, sorted by two separate questions — strict or slack, and how many letters survive to what power. Knowing one answer settles nothing about the other.13 min · 12 parts

Part 2

Solving one in a single variable

15 minWhy testing values one by one is not a method, and what replaces itSubstitute zero into an inequality that rises then falls, get a false verdict, and stop on habit — and seven real solutions further along are thrown away unseen.15 min · 13 parts

15 minThe one rule that differs from equation-solving, and the reason it differsAdd the same number to both sides of an inequality, checked across seventy-eight pairs, and not one changes order. Multiply by a negative, and all seventy-eight swap.15 min · 14 parts

13 minDrawing the answer as a piece of the number line, hollow circle or solidScore a solved inequality's drawing against a hundred and one values. The wrong stroke direction misses a hundred of them; the wrong circle style misses one — the endpoint.13 min · 13 parts

What you will be able to do

Give two situations that cannot be written as equations, and say what blocks the equality in each
State the four relations that turn two expressions into an inequality
Substitute a stated value into an inequality and report whether the statement comes out true
State the two rules the chapter gives for rewriting an inequality, and say which one differs from its equation counterpart
Solve a linear inequality and draw its answer on a number line with the correct endpoint marking

What this chapter assumes you already know

Forming an expression in one or two letters from a word description, and reading it back as a quantity
Solving a linear equation in one variable, and what it means for an equation to have exactly one solution
Whole numbers versus fractions, and the idea that some quantities can only be counted in whole units
Reading the four order symbols aloud: less than, greater than, and their two "or equal" companions
Reading and writing expressions of the forms ax + b and ax + by, and knowing which letters are the coefficients and which the variables
What "degree" means for a polynomial expression in one letter
That a statement with no letter in it is already either true or false
The natural numbers, the integers and the real numbers as three different collections, and which sits inside which

It builds directly on Why "well-defined" is the whole difference between a set and a heap, Listing the members versus stating the property they share, A set with nothing in it, and sets you cannot finish listing, The number systems as a chain of containments, and intervals as pieces of R and Union and intersection, and what it means for two sets to miss each other entirely.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

"≤ is just < being cautious."
"If ₹200 is available, ₹200 is what gets spent."
"Both are 'less than something', so both take <."
"An inequality is a vaguer statement than an equation."
"x could be any number here."
"The chapter will show me how to solve Reshma's two-letter statement."
"Strict versus slack is about how big the answer is."
"3 < 5 is not a real inequality, there is no letter in it."