Inequalities with addition and subtraction of fractions

Learning Objectives Solve one-step inequalities involving the addition of fractions. Solve one-step inequalities involving the subtraction of fractions. Isolate a variable in an inequality by applying the correct inverse operation with fractions. Find the least common denominator to combine fractions within an inequality. Represent the solution set of a fractional inequality on a number line. Verify the solution to an inequality by substituting a valid test value from the solution set. Translate a real-world scenario into a one-step inequality with fractions and solve it. A structural beam's length can be at most 15 and 1/2 meters. After cutting off a piece, it is now 14 and 3/4 meters. What is the maximum possible length of the piece that was removed? 📐 This tutori...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol, indicating that one expression is less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥) another.x + 1/2 > 3/4 Solution SetThe set of all values for a variable that make an inequality true. Unlike an equation which often has one solution, an inequality typically has an infinite number of solutions.For x > 2, the solution set includes 3, 5, 2.1, and 100, but not 2 or 1. Inverse OperationAn operation that reverses the effect of another operation. Addition and subtraction are inverse operations, used to isolate a variable.To undo adding 1/4 to a variable, you subtract 1/4 from both sides of the inequality. Least Common Denominator...

Addition Property of Inequality If a < b, then a + c < b + c. The same property holds true for >, ≤, and ≥. You can add the same number (including a fraction) to both sides of an inequality without changing the direction of the inequality symbol. This is used to cancel out a subtracted term. Subtraction Property of Inequality If a < b, then a - c < b - c. The same property holds true for >, ≤, and ≥. You can subtract the same number (including a fraction) from both sides of an inequality without changing the direction of the inequality symbol. This is used to cancel out an added term.