Solving Multi-step Inequalities

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

To isolate a variable in an inequality, perform inverse operations on both sides of the inequality, similar to solving an equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Reversing the inequality sign means changing '<' to '>' or '≤' to '≥' when you multiply or divide both sides of the inequality by a negative number.

To graph the solution of an inequality, draw a number line, use an open circle for '<' or '>' and a closed circle for '≤' or '≥', and shade the region that represents the solution set.

A strict inequality (e.g., '<' or '>') does not include the endpoint, while a non-strict inequality (e.g., '≤' or '≥') includes the endpoint.

A compound inequality consists of two or more inequalities joined by 'and' or 'or', representing a range of values that satisfy all the inequalities.