Solve linear inequalities

Learning Objectives Solve one-variable linear inequalities using algebraic properties. Correctly apply the rule for reversing the inequality symbol when multiplying or dividing by a negative number. Represent the solution set of a linear inequality on a number line. Write the solution set of a linear inequality using interval notation. Solve compound linear inequalities involving 'and' (conjunctions) and 'or' (disjunctions). Translate a real-world scenario into a linear inequality and solve it. What's the minimum average speed you need to maintain to finish a 200km road trip in under 3 hours? 🚗 That's a question you can answer by solving a linear inequality! This tutorial revisits the essential algebraic skill of solving linear inequalities. W...

TermDefinitionExample Linear InequalityA mathematical statement that compares two linear expressions using an inequality symbol (<, >, ≤, ≥). It shows that the two expressions are not strictly equal.3x - 7 > 5 Solution SetThe set of all numbers that, when substituted for the variable, make the inequality a true statement.For x > 4, the solution set includes 5, 6, 4.1, and all other numbers greater than 4. Number Line RepresentationA graphical way to display the solution set. An open circle is used for < and >, and a closed (filled) circle is used for ≤ and ≥.The graph of x ≤ 2 is a closed circle at 2 with an arrow pointing to the left along the number line. Interval NotationA compact way to write the solution set using parentheses () for endpoints that are not included a...

Addition and Subtraction Property of Inequality If a > b, then a + c > b + c and a - c > b - c. You can add or subtract the same value from both sides of an inequality without changing the direction of the inequality symbol. This works the same as with equations. Multiplication and Division Property of Inequality Case 1 (c > 0): If a > b, then ac > bc. \nCase 2 (c < 0): If a > b, then ac < bc. When you multiply or divide both sides by a POSITIVE number, the inequality symbol stays the same. When you multiply or divide both sides by a NEGATIVE number, you MUST REVERSE the inequality symbol (e.g., > becomes <).