Solutions to inequalities

Learning Objectives Define the solution set of an inequality. Determine if a given number is a solution to an inequality by using substitution. Solve one-step and two-step linear inequalities in one variable. Correctly apply the rule for multiplying or dividing an inequality by a negative number. Represent the solution set of an inequality on a number line using open and closed circles. Translate simple real-world scenarios into one-variable inequalities. Need to score at least an 80 on your next test to get a B? You're already thinking about inequalities! 📈 Unlike equations that usually have one answer, inequalities have a whole range of possible solutions. In this lesson, we'll explore how to find this range of solutions, called the solution set, and how to sho...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol. It shows that the two sides are not necessarily equal.x + 4 > 10 is an inequality. It reads 'x plus 4 is greater than 10'. Solution of an InequalityAny value of the variable that makes the inequality a true statement.In the inequality x > 6, the number 7 is a solution because 7 > 6 is true. The number 5 is not a solution because 5 > 6 is false. Solution SetThe complete set of all numbers that are solutions to an inequality.For x > 6, the solution set includes 6.1, 7, 8, 100, and all other numbers greater than 6. Inequality SymbolsThe symbols used to compare quantities: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater th...

Addition and Subtraction Properties of Inequality If a > b, then a + c > b + c and a - c > b - c. You can add or subtract the same number on both sides of an inequality without changing the direction of the inequality symbol. This works the same as it does for equations. Multiplication and Division Properties of Inequality (The Golden Rule) 1. If a > b and c > 0, then ac > bc. 2. If a > b and c < 0, then ac < bc. When you multiply or divide both sides of an inequality by a POSITIVE number, the symbol stays the same. When you multiply or divide both sides by a NEGATIVE number, you MUST REVERSE the direction of the inequality symbol.