Inequalities with addition and subtraction of fractions and mixed numbers

Learning Objectives Define and identify inequality symbols. Accurately add and subtract fractions with like and unlike denominators. Convert between mixed numbers and improper fractions proficiently. Solve one-step inequalities involving addition of fractions and mixed numbers. Solve one-step inequalities involving subtraction of fractions and mixed numbers. Graph the solution sets of inequalities on a number line. Apply inverse operations to isolate variables in inequalities. Ever wonder how to compare quantities that aren't exactly equal, especially when they involve tricky fractions? 🤔 In this lesson, you'll learn how to solve inequalities where you add or subtract fractions and mixed numbers. This skill is crucial for understanding real-world situations whe...

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).$x + \frac{1}{2} > 2$ FractionA number representing a part of a whole, written as a numerator over a denominator (e.g., $\frac{a}{b}$).$\frac{3}{4}$ (three-fourths) Mixed NumberA number consisting of a whole number and a proper fraction.$2\frac{1}{3}$ (two and one-third) Common DenominatorA common multiple of the denominators of two or more fractions, necessary for adding or subtracting them.For $\frac{1}{2}$ and $\frac{1}{3}$, the common denominator is 6. Inverse OperationsOperations that undo each other. For inequalities, addition is the inverse of subtraction, and vice versa.To solv...

Addition Property of Inequality If $a < b$, then $a + c < b + c$. The same applies to >, ≤, and ≥. You can add the same number or expression to both sides of an inequality without changing the direction of the inequality sign. This helps isolate the variable. Subtraction Property of Inequality If $a < b$, then $a - c < b - c$. The same applies to >, ≤, and ≥. You can subtract the same number or expression from both sides of an inequality without changing the direction of the inequality sign. This also helps isolate the variable. Adding/Subtracting Fractions Rule To add or subtract fractions, they must have a common denominator. If they don't, find the least common denominator (LCD), convert the fractions, then add or subtract the numerators: $\fr...