Solve inequalities using addition and subtraction (Advanced)

Learning Objectives Identify and interpret inequality symbols (<, >, ≤, ≥). Understand that an inequality has a set of solutions, not just one. Solve one-variable inequalities involving positive and negative integers using the Addition Property of Inequality. Solve one-variable inequalities involving positive and negative integers using the Subtraction Property of Inequality. Graph the solution sets of inequalities on a number line, correctly using open and closed circles. Translate simple real-world scenarios into one-variable inequalities. Ever wonder how many cookies you can eat without going over your daily sugar limit? 🍪 Or how many minutes you can play a game without missing your bedtime? These are all about inequalities! In this lesson, you'll learn how t...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥).x + 3 < 10 Solution to an InequalityAny value of the variable that makes the inequality true. Unlike equations, inequalities often have many solutions.For x < 7, numbers like 6, 5, 0, -10 are all solutions. Addition Property of InequalityAdding the same number to both sides of an inequality does not change the truth of the inequality.If x - 5 > 2, then x - 5 + 5 > 2 + 5, which means x > 7. Subtraction Property of InequalitySubtracting the same number from both sides of an inequality does not change the truth of the inequality.If x + 4 ≤ 9, then x + 4 - 4 ≤ 9 - 4, which means x ≤ 5. Number LineA line on which numbers are marked at regular inter...

Addition Property of Inequality If $a < b$, then $a + c < b + c$. This also applies to $>, \le, \ge$. To isolate a variable that is being subtracted, add the same number to both sides of the inequality. Subtraction Property of Inequality If $a < b$, then $a - c < b - c$. This also applies to $>, \le, \ge$. To isolate a variable that is being added, subtract the same number from both sides of the inequality. Graphing Solutions on a Number Line For $<$ or $>$, use an **open circle** on the number representing the boundary. For $\le$ or $\ge$, use a **closed circle** on the number representing the boundary. Draw an arrow pointing in the direction of the solution set (left for less than, right for greater than). This rule helps visualize all possi...