Linear Inequalities

To solve inequalities, we rely on fundamental properties discussed in ==Section on Inequalities==. Two of the most important are:

• We can add (or subtract) the same quantity from both sides without changing the direction of the inequality.
• We can multiply (or divide) both sides by a positive quantity, without changing the direction of the inequality.
• If we multiply or divide both sides of an inequality by a negative quantity, the direction of the inequality reverses (see ==Section on Inequalities==).

Linear inequalities are often easy to solve. We just need to isolate the variable on one side of the inequality sign.

• For the last example, note thatmeansIn fact, we have to solve two inequalities.