Inequalities with decimal division

Learning Objectives Identify and interpret inequality symbols. Accurately perform division involving decimal numbers. Solve one-step inequalities involving division by positive and negative decimals. Solve multi-step inequalities that include decimal division. Correctly graph the solution set of an inequality on a number line. Verify solutions to inequalities involving decimal division. Apply inequalities with decimal division to solve real-world problems. Ever wondered how many friends you can invite to a party if you have a budget of $50 and each guest costs $3.75? 🥳 In this lesson, you'll learn how to solve mathematical statements called inequalities, especially when they involve dividing by decimal numbers. Understanding this is crucial for making decisions when...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol (e.g., <, >, ≤, ≥) to show that one is not necessarily equal to the other.$x < 5$ (x is less than 5) VariableA symbol, usually a letter, that represents an unknown numerical value in an equation or inequality.In $0.5x > 10$, 'x' is the variable. Decimal NumberA number that contains a decimal point, representing a fractional part of a whole number.$0.25$, $3.7$, $-1.5$ Solution SetThe set of all values that make an inequality true. Unlike equations, inequalities often have infinitely many solutions.For $x > 3$, the solution set includes all numbers greater than 3 (e.g., 3.1, 4, 100). Number LineA visual representation of numbers as points on a straight...

Division Property of Inequality (Positive Divisor) If $a < b$ and $c > 0$, then $\frac{a}{c} < \frac{b}{c}$. The inequality sign remains the same. When you divide both sides of an inequality by a positive number (including positive decimals), the direction of the inequality symbol does not change. Division Property of Inequality (Negative Divisor) If $a < b$ and $c < 0$, then $\frac{a}{c} > \frac{b}{c}$. The inequality sign reverses. When you divide both sides of an inequality by a negative number (including negative decimals), you MUST reverse the direction of the inequality symbol. Isolating the Variable To solve an inequality, perform inverse operations to get the variable by itself on one side of the inequality symbol. This is similar to solving...