📝 Practice Worksheets
🔑 Key Concepts
- When solving inequalities, use the same inverse operations you would use for equations.
- Distribute first if a number is outside parentheses.
- If you divide or multiply both sides by a negative number, the inequality symbol must reverse.
- After isolating the variable, the solution tells which values make the inequality true.
💡 Main Idea
This lesson focuses on solving inequalities that involve distribution, combining like terms, and dividing by negative values. The steps are very similar to solving equations, but students must pay close attention when a negative number is used to isolate the variable, because that is when the inequality sign flips.
🧠 Math Vocabulary
- Inequality: a mathematical statement that compares two quantities using symbols such as \( < \), \( > \), \( \le \), or \( \ge \).
- Distribute: multiply a factor across the terms inside parentheses.
- Inverse operations: operations that undo each other, such as addition and subtraction or multiplication and division.
- Reverse the inequality: change the direction of the symbol when multiplying or dividing both sides by a negative number.
- Solution: a value that makes the inequality true.
📚 What You Should Already Know
Students should already know how to distribute, combine like terms, and solve basic equations using inverse operations. It also helps to understand why the inequality sign flips when dividing by a negative number.
🚀 What Comes Next
After solving inequalities like these, students can graph their solution sets on a number line, solve inequalities with variables on both sides, and apply these skills in word problems and real-world situations.
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