Graph solutions two-step linear inequalities

Learning Objectives Solve two-step linear inequalities for a single variable using inverse operations. Identify when to reverse the inequality symbol when multiplying or dividing by a negative number. Accurately represent the solution set of an inequality on a number line. Differentiate between using an open circle (<, >) and a closed circle (≤, ≥) on a number line graph. Correctly shade the number line to indicate the direction of the infinite solution set. Verify a point within the graphed solution set to confirm its validity. Need to save at least $50 for concert tickets and already have $10? If you earn $8 per hour, how many hours do you need to work? 🤔 Let's find out! This tutorial will teach you how to solve two-step linear inequalities and, most important...

TermDefinitionExample Linear InequalityA mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥) instead of an equals sign. A two-step inequality requires two inverse operations to solve.3x + 7 ≤ 16 Solution SetThe collection of all numbers that make the inequality true. For linear inequalities, this is usually an infinite range of numbers.For x > 4, the solution set includes 5, 6, 4.1, and any other number greater than 4. Inverse OperationsOperations that undo each other. Addition and subtraction are inverses; multiplication and division are inverses.To undo adding 5, you subtract 5. To undo multiplying by 2, you divide by 2. Number Line GraphA visual representation of an inequality's solution set on a line, using a circle and a shaded a...

Addition/Subtraction Property of Inequality If a < b, then a + c < b + c and a - c < b - c. You can add or subtract the same number from both sides of an inequality without changing the direction of the inequality symbol. This is the first step in solving a two-step inequality. Multiplication/Division Property of Inequality (Positive Number) If a < b and c > 0, then ac < bc and a/c < b/c. You can multiply or divide both sides of an inequality by the same POSITIVE number without changing the direction of the inequality symbol. The Golden Rule: Multiplying/Dividing by a Negative Number If a < b and c < 0, then ac > bc and a/c > b/c. This is the most important rule. When you multiply or divide both sides of an inequality by a NEGATIVE nu...