Solving Linear Inequalities

Consider the inequality:

Inequality

Solve by following these steps:

1. Remove the brackets.

Inequality

2. Remove the parentheses.

Inequality

3. Remove the denominators.

Inequality

Inequality

4. Group the terms of x to one side of the inequality and the independent terms to the other.

Inequality

5. Calculate:

Inequality

6.Because the coefficient of x is negative, multiply by −1 so that it will change the sense of the inequality.

Inequality

7. Work out the value of the unknown.

Inequality

8.The solution is an inequality, but it can also be expressed:

Graphically:

Greater than or Equal to 3

As an interval:

[3, +∞)


Examples

1Inequality Exercise

Inequality Operations

Inequality Operations

Inequality Solution

Greater than 1

(1, ∞)

2Inequality Exercise

Inequality Operations

Inequality Operations

Inequality Operations

Inequality Operations

Inequality Solution

Greater than or Equal to 1/4

Inequality Solution

3Inequality Exercise

Inequality Operations

Inequality Operations

Inequality Operations

Inequality Operations

Inequality Solution

Inequality Solution