Multi-step inequalities with decimals

Learning Objectives Solve multi-step inequalities involving decimal coefficients and constants. Accurately apply inverse operations to isolate variables in inequalities with decimals. Correctly reverse the inequality sign when multiplying or dividing by a negative decimal. Graph the solution set of multi-step inequalities with decimals on a number line. Check the validity of their solutions for multi-step inequalities with decimals. Translate real-world scenarios into multi-step inequalities with decimals and solve them. Ever wondered how many hours you can work at a part-time job to earn at least $150, if you make $8.25 per hour and have $25 deducted for supplies? 💰 Let's find out! In this lesson, you'll learn how to solve inequalities that require more than one...

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 + 3.5 > 7.2 Solution SetThe set of all values for the variable that make an inequality true. Unlike equations, inequalities often have infinitely many solutions.For x > 2.5, the solution set includes all numbers greater than 2.5 (e.g., 2.6, 3, 10.1). VariableA symbol, usually a letter, that represents an unknown number or quantity in a mathematical expression or equation/inequality.In the inequality 2.5y - 1.0 ≤ 4.0, 'y' is the variable. DecimalA number that uses a decimal point to represent a whole number and fractional parts (tenths, hundredths, etc.).Numbers like 0.5,...

Addition/Subtraction Property of Inequality If $a < b$, then $a + c < b + c$ and $a - c < b - c$. This also applies to >, ≤, and ≥. You can add or subtract the same number (including decimals) to both sides of an inequality without changing the direction of the inequality sign. Multiplication/Division Property of Inequality (Positive Number) If $a < b$ and $c > 0$, then $ac < bc$ and $\frac{a}{c} < \frac{b}{c}$. This also applies to >, ≤, and ≥. You can multiply or divide both sides of an inequality by the same positive number (including decimals) without changing the direction of the inequality sign. Multiplication/Division Property of Inequality (Negative Number) If $a < b$ and $c < 0$, then $ac > bc$ and $\frac{a}{c} > \frac{b}...