Linear Inequalities

The symbols used in inequalities are:


Example One

Solve:
(a) x less than 3
(b) x less than or equal to 5
(c) x greater than 2
(d) x + 4 less than 6
(e) 2x greater than 10
(f) –2x greater than 10

Answers:
(a) x < 3

(b) x ≤ 5

(c) x > 2

(d) x + 4 < 6
x < 6 – 4
x < 2

(e) 2x > 10
x > 5

(f) –2x > 10
x < –5
Notice that when you divide by a negative number, the sign changes.

Questions - Solve these Inequalities

Q1. x + 3 < 7
Q2. –3x < 6

Answers
A1. x < 4
A2. x > –2

Before viewing the next part, it would be helpful to learn Linear Graphs

Example Two

(a) Graph y < x + 3.
(b) Plot the point (5,2) to determine which side of the graph should be shaded as the "less than" side.

Answer:
(a)

x012
y = x + 3345

(b) y < x + 3
2 < 5 + 3
This is correct so the point (5,2) is on the "less than" side and we will shade this side.