Example Card: Multiplying by a Negative Number
Solve inequalities involving multiplication or division by a negative number, flipping the inequality sign to maintain a true statement in Grade 9 Algebra.
Key Concepts
A single negative sign can flip this entire problem on its head. Let's see how the Multiplication Property of Inequality for $c < 0$ works.
Example Problem Solve, graph, and check the solution for the inequality $\frac{ x}{3} < 4$.
Step by Step 1. Start with the given inequality. $$ \frac{ x}{3} < 4 $$ 2. To isolate $x$, we need to multiply both sides by $ 3$. Because we are multiplying by a negative number, we must reverse the inequality symbol. $$ ( 3)\frac{ x}{3} 4( 3) \quad \text{Multiplication Property of Inequality for } c < 0 $$ 3. Simplify the expression to find the solution. $$ x 12 \quad \text{Simplify.} $$ 4. Graph the solution on a number line. This requires an open circle at $ 12$ and an arrow pointing to the right, indicating all numbers greater than $ 12$.
Common Questions
What is Example Card: Multiplying by a Negative Number?
Example Card: Multiplying by a Negative Number is a key concept in Grade 9 math. It involves applying specific rules and properties to simplify expressions, solve equations, or analyze mathematical relationships. Understanding this topic builds foundational skills needed for higher-level algebra and beyond.
How is Example Card: Multiplying by a Negative Number used in real-world applications?
Example Card: Multiplying by a Negative Number appears in practical contexts such as financial calculations, engineering problems, and data analysis. Mastering this skill helps students model and solve problems they will encounter in science, technology, and everyday decision-making situations.
What are common mistakes when working with Example Card: Multiplying by a Negative Number?
Common errors include forgetting to apply rules to all terms, sign errors when working with negatives, and skipping verification steps. Always double-check by substituting answers back into the original problem and reviewing each algebraic step carefully.