Algebraic inequalities and systems of inequalities

Algebraic inequalities involve expressions with variables and inequality signs. Solving an inequality means finding all values of the variable that make the inequality true. A system of inequalities is a set of inequalities that must all be satisfied at once. Solutions to systems are values (or sets of values) that make every inequality in the system true.

Important properties

• You can add or subtract the same value from both sides of an inequality without changing its truth.

• You can multiply or divide both sides by a positive number without changing the direction of the inequality.

• If you multiply or divide both sides by a negative number, you must reverse the direction of the inequality.

• The solution to a system of inequalities is the intersection of the solution sets of each individual inequality.