**Definition of Linear Inequality**

- A Linear Inequality involves a linear expression in two variables by using any of the relational symbols such as <,>, ≤ or ≥

**More about Linear Inequality**

- A linear inequality divides a plane into two parts.
- If the boundary line is solid, then the linear inequality must be either ≥ or ≤.
- If the boundary line is dotted, then the linear inequality must be either > or <.>

**Example of Linear Inequality**

- As the boundary line in the above graph is a solid line, the inequality must be either ≥ or ≤. Since the region below the line is shaded, the inequality should be ‘≤’. We can notice that the line y = - 2x + 4 is included in the graph; therefore, the inequality is y ≤ - 2x + 4. Any point in the shaded plane is a solution and even the points that fall on the line are also solutions to the inequality.
- 4x + 6y ≤ 12, x + 6 ≥ 14, 2x - 6y < 12="" +="" 2x,="" 9y="">< 12="" +="" 2x="" are="" the="" examples="" of="" linear="" inequalities.="">

**Solved Example on Linear Inequality**

Which of the graphs best suits the inequality y < x="" -="">

Choices:

A. Graph 1

B. Graph 2

C. Graph 3

D. Graph 4

Correct Answer: A

Solution:

Step 1:Since the inequality ‘involves less than’ (<), use="" dashed="" boundary="" line="" to="" graph="" the="" inequality="" y="">< x="" -="" 4="" as="" in="" the="" below="" shown="">

Step 2:Test a point, which is not on the boundary line.

Test (0, 0) in the inequality.

y < x="" –="" 4="" [substitute.]="">

0 < 0="" –="">

0 < -="" 4="">

Step 3: Since the inequality is false for (0, 0), shade the region that does not contain (0, 0).

Step 4:Therefore, Graph 1 best suit the inequality y < x="" -="">

**Related Terms for Linear Inequality**

- Graphs
- Inequality
- Line
- Linear
- Plane
- Side
- Solution
- Variable