Solving Inequalities

Students will be able to solve inequalities and graph them

on a number line.

Equations and Inequalities 2FHS

Solving InequalitiesTo solve inequalities, we follow the same procedures

that we do in solving equations. But Warning! -There is one exception.

Whenever you multiply or divide by a negative number, you always change the direction of the inequality sign.

Here are some examples:

2 6

2 2

x

2 6x2 6

2 2

x2 6 x

3x 3 x

The difference between these two problems is that we are dividing by a negative number.

Equations and Inequalities 3FHS

Graphing Inequalities

• We need to graph our answer on the number line.

• If we have a < or > sign, we will put an open circle on that number on the number line.

• If we have a ≤ or a ≥, then we put a solid circle on that number on the number line.

• Then we shade the number line in the correct direction.

Equations and Inequalities 4FHS

Examples

Here are some examples to graph.

x > 3

x < – 3

| | | | | | | -2 -1 0 1 2 3 4

| | | | | | | -4 -3 -2 -1 0 1 2

Equations and Inequalities 5FHS

Here are some more examples:

x ≤ 2

y ≥ -1

| | | | | | | -3 -2 -1 0 1 2 3

| | | | | | | -3 -2 -1 0 1 2 3

Examples