# Solving inequalities

The process to solve inequalities is the same as the process to solve equations, which uses to keep the equation or inequality balanced. Instead of using an equals sign, however, the inequality symbol is used throughout.

### Example

Solve the inequality .

The inequality will be solved when is isolated on one side of the inequality. This can be done by using inverse operations at each stage of the process.

The final answer is , which means can be any value that is bigger than -2, not including -2 itself. If this answer was to be placed on a number line, an open circle would be needed at -2 with a line indicating the numbers that are greater than 2.

Question

Solve the inequality . Show the answer on a number line.

Expand the bracket:

Subtract 4 from each side:

Divide each side by 4:

To show this answer on a number line, put a closed circle at and indicate the numbers that are less than .

Extra care should be taken when the unknown in an inequality has a negative . Use an inverse operation to make the coefficient of the unknown positive.

Question

Solve the inequality . Show the answer on a number line.

Expand the bracket:

The unknown has a coefficient of -3, so now add to both sides of the inequality:

Subtract 6 from each side:

Now divide both sides by 3:

, which can also be written as (reading from right to left).

To show this answer on a number line, put an open circle at 1 and indicate the numbers greater than 1.