# 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.