Linear Inequalities
The symbols used in inequalities are:
- < less than
- ≤ less than or equal to
- > greater than
- ≥ greater than or equal to.
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)
| x | 0 | 1 | 2 |
| y = x + 3 | 3 | 4 | 5 |
(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.
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