Inequalities with decimal multiplication

Learning Objectives Accurately multiply decimals. Apply the multiplication property of inequality to solve one-step inequalities involving decimals. Correctly reverse the inequality sign when multiplying by a negative decimal. Graph the solution set of an inequality with decimal multiplication on a number line. Check their solutions for inequalities involving decimal multiplication. Identify real-world scenarios where inequalities with decimal multiplication are applicable. Ever wonder how stores calculate discounts or how much of a ingredient you can use without going over a limit? 💰 This lesson will show you how to solve problems where quantities are multiplied by decimals, but with a twist! In this lesson, you'll learn how to solve inequalities where a variable is...

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.$2x < 10$ or $y + 3 \ge 7$ DecimalA number that contains a decimal point, representing a part of a whole number. Decimals are often used to represent fractions or percentages.$0.5$, $3.14$, $-1.25$ Multiplication Property of InequalityA rule stating how an inequality behaves when both sides are multiplied by the same number. The direction of the inequality sign depends on whether the multiplier is positive or negative.If $x < 5$, then $2x < 10$ (multiplying by positive 2). If $x < 5$, then $-2x > -10$ (multiplying by negative 2, sign flips). Solution SetThe set of all numbers that ma...

Multiplication Property of Inequality (Positive Multiplier) If $a < b$ and $c > 0$, then $ac < bc$. The inequality sign remains the same. When you multiply both sides of an inequality by a positive number (including positive decimals), the direction of the inequality symbol does not change. This also applies to >, ≤, and ≥. Multiplication Property of Inequality (Negative Multiplier) If $a < b$ and $c < 0$, then $ac > bc$. The inequality sign reverses. When you multiply both sides of an inequality by a negative number (including negative decimals), you MUST reverse the direction of the inequality symbol. This is a critical rule to remember! Solving One-Step Inequalities with Decimal Multiplication To solve $ax < b$ (or $ax > b$, $ax \le b$, $a...