Inequalities with addition and subtraction: set 2

Learning Objectives Identify and interpret inequality symbols (<, >, ≤, ≥). Solve one-step inequalities involving addition using inverse operations. Solve one-step inequalities involving subtraction using inverse operations. Represent the solution sets of inequalities on a number line using open and closed circles. Check the validity of solutions for inequalities. Translate simple real-world scenarios into inequalities with addition or subtraction. Have you ever needed to know if you have *at least* a certain amount of money 💰 or if a temperature is *below* a specific point? That's where inequalities come in! In this lesson, we'll build on our understanding of inequalities by learning how to solve them using addition and subtraction. You'll discover ho...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).x + 5 > 10 VariableA letter or symbol (like x or y) used to represent an unknown number or a range of numbers.In y - 3 ≤ 7, y is the variable. Solution SetThe set of all numbers that make an inequality true. Unlike equations, inequalities often have many solutions.For x > 5, the solution set includes 6, 7, 8, and all numbers greater than 5. Inverse OperationsOperations that undo each other, like addition and subtraction. We use them to isolate the variable.To undo + 7, we use - 7. Number LineA visual representation of numbers in order, used to graph the solution set of an inequality...

Addition Property of Inequality If $a < b$, then $a + c < b + c$. (Also applies to >, ≤, ≥) Adding the same number to both sides of an inequality does not change the direction of the inequality sign. Use this when you need to 'undo' a subtraction from the variable by adding the same amount to both sides. Subtraction Property of Inequality If $a < b$, then $a - c < b - c$. (Also applies to >, ≤, ≥) Subtracting the same number from both sides of an inequality does not change the direction of the inequality sign. Use this when you need to 'undo' an addition to the variable by subtracting the same amount from both sides. Graphing Solutions on a Number Line Use an open circle for < or >, and a closed circle for ≤ or ≥. Shade the n...