Linear Inequations — Part 1: Replacement sets and solving: visual lesson, ICSE Class 10 Mathematics

Lesson

Linear Inequations, Part 1

An equation has one answer; an inequation usually has many. Which ones count depends on the replacement set.

In this lesson you will

Dots at $0, 1, 2$ and $3$: the whole numbers less than $4$.

Concept

Read the four inequality signs
Use the replacement sets $\mathbb{N}$ , $\mathbb{W}$ , $\mathbb{Z}$ and $\mathbb{R}$
Solve a linear inequation step by step
Reverse the sign when multiplying or dividing by a negative number
Write the answer in roster or set-builder form

Concept

A linear inequation in one variable compares two expressions such as $3x + 2$ and $14$ with one of four signs.

The sign decides whether the boundary number belongs.
Sign	Read as	Example	Is $x = 3$ a solution?
$<$	is less than	$x < 3$	no
$\le$	is less than or equal to	$x \le 3$	yes
$>$	is greater than	$x > 3$	no
$\ge$	is greater than or equal to	$x \ge 3$	yes