Solve two-step inequalities

Learning Objectives Identify and interpret inequality symbols. Apply inverse operations to isolate a variable in a two-step inequality. Solve two-step inequalities involving addition, subtraction, multiplication, and division. Correctly apply the rule for reversing the inequality sign when multiplying or dividing by a negative number. Graph the solution set of a two-step inequality on a number line. Check the validity of solutions for two-step inequalities. Ever wonder how stores decide how many items to stock based on sales goals? Or how much money you can spend without going over budget? 💰 Inequalities help us figure out 'at least,' 'at most,' and 'within a range'! In this lesson, you'll learn how to solve inequalities that require two...

TermDefinitionExample InequalityA mathematical statement comparing two expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).x + 3 > 5 Solution to an InequalityAny value(s) for the variable that make the inequality true. Unlike equations, inequalities often have infinitely many solutions.For x > 2, x=3, x=4.5, x=100 are all solutions. Inverse OperationsOperations that undo each other (e.g., addition undoes subtraction, multiplication undoes division). Used to isolate the variable.To undo +5, you use -5. To undo *2, you use /2. VariableA symbol, usually a letter, that represents an unknown quantity or a quantity that can change.In 2x - 7 < 15, 'x' is the variable. ConstantA value that does not cha...

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 truth of the inequality or the direction of the inequality sign. Use this property to move constant terms away from the variable term. Multiplication/Division Property of Inequality If $a < b$ and $c > 0$, then $ac < bc$ and $a/c < b/c$. If $a < b$ and $c < 0$, then $ac > bc$ and $a/c > b/c$. If you multiply or divide both sides of an inequality by a *positive* number, the inequality sign remains the same. If you multiply or divide both sides by a *negative* number, you *must reverse the direction of the inequality sign*. Use this property to isolate the va...