Solve one-step inequalities

Learning Objectives Identify and define key terms related to inequalities. Solve one-step inequalities involving addition and subtraction. Solve one-step inequalities involving multiplication and division by positive numbers. Solve one-step inequalities involving multiplication and division by negative numbers, correctly reversing the inequality sign. Graph the solution set of a one-step inequality on a number line. Check solutions to one-step inequalities. Ever wonder how stores decide how many items to stock, or how much money you can spend without going over budget? 🤔 Inequalities help us figure out "at least" or "at most" situations! In this lesson, you'll learn how to solve simple inequalities that only require one step. Understanding these wi...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol ($<, >, \le, \ge$).$x + 3 < 10$ Solution to an InequalityAny value(s) of the variable that makes the inequality a true statement. Unlike equations, inequalities often have many solutions.For $x < 7$, values like $x=1, 0, -5$ are all solutions. Graphing an InequalityRepresenting the solution set of an inequality on a number line using open/closed circles and shading.For $x > 3$, an open circle at 3 with shading to the right. Inverse OperationsOperations that undo each other (e.g., addition undoes subtraction, multiplication undoes division). These are used to isolate the variable.To solve $x - 5 > 2$, you use the inverse operation of adding 5 to both sides. Va...

Addition/Subtraction Property of Inequality If $a < b$, then $a + c < b + c$ and $a - c < b - c$. Adding or subtracting the same number from both sides of an inequality does not change the direction of the inequality sign. Use this rule to isolate the variable when a constant is being added to or subtracted from it. Multiplication/Division Property of Inequality (Positive Number) If $a < b$ and $c > 0$, then $ac < bc$ and $\frac{a}{c} < \frac{b}{c}$. Multiplying or dividing both sides of an inequality by the same *positive* number does not change the direction of the inequality sign. Use this rule to isolate the variable when it's multiplied or divided by a positive coefficient. Multiplication/Division Property of Inequality (Negative Number)...