Example Card: Simplifying and Solving 'AND' Inequalities
Master Simplifying and Solving 'AND' Inequalities in Grade 9 Algebra 1. Let's untangle this compact inequality by applying our rules to all three parts at once.
Key Concepts
Let's untangle this compact inequality by applying our rules to all three parts at once.
Example Problem Solve the inequality $ 21 \le 3(2x 5) \le 33$ and justify each step.
Step by Step 1. Start with the given inequality. $$ 21 \le 3(2x 5) \le 33 $$ 2. First, use the Distributive Property on the middle part of the inequality. $$ 21 \le 6x 15 \le 33 $$ 3. Now, apply the Addition Property of Inequality by adding $15$ to all three parts to start isolating the variable term. $$ 21 + 15 \le 6x 15 + 15 \le 33 + 15 $$ 4. Simplify each part of the inequality. $$ 6 \le 6x \le 48 $$ 5. Use the Division Property of Inequality by dividing all three parts by $6$ to solve for $x$. $$ \frac{ 6}{6} \le \frac{6x}{6} \le \frac{48}{6} $$ 6. Simplify to find the final solution. $$ 1 \le x \le 8 $$.
Common Questions
What is Simplifying and Solving 'AND' Inequalities in Algebra 1?
Simplifying and Solving 'AND' Inequalities is a core Grade 9 Algebra 1 concept covering properties and applications.
How do you work with Simplifying and Solving 'AND' Inequalities in Grade 9 math?
Solving an inequality like this is like finding a 'Goldilocks' zone for 'x'—it can't be too small or too big, it has to be just right, somewhere between two numbers. Think of it as a balancing act. Your goal is to get all by itself in the middle. To keep everything fair and balanced, whatever you do.
What are common mistakes when learning Simplifying and Solving 'AND' Inequalities?
Solving an inequality like this is like finding a 'Goldilocks' zone for 'x'—it can't be too small or too big, it has to be just right, somewhere between two numbers. Think of it as a balancing act. Your goal is to get all by itself in the middle. To keep everything fair and balanced, whatever you do to the middle part, you must do to the other two.