Linear inequalities

Linear Inequalities

< Less than

> More than

≤ Less than or Equal to

≥ More than or Equal to

Open circle > < 

Close circle ≥ ≤

Example:-

1. Solve the following inequalities

a) x – 5 ≥ 2 (x + 6)

= x – 5 ≥ 2 x + 12

= x – 2x ≥ 12 + 5

= -x ≥ 17

= x ≤ 17

b) –x + 2 < 6 (x – 3)

= -x + 2< 6x – 18

= -x – 6x < -18 – 2

= -7x < -20

= x > -20/-7

= x > 2.8

2. -14 ≤ 2x

= x -14 ≤ 2

= x ≤ 2 + 14

= x ≤ 16

3. 3x – 1 ≤ 14

= 3x ≤ 14 -1

= 3x ≤ 15

= x ≤ 15/3

= x ≤ 5