📝 Practice Worksheets
🔑 Key Concepts
- Solving an inequality follows many of the same steps as solving an equation.
- Use inverse operations to isolate the variable.
- When multiplying or dividing by a negative number, reverse the inequality symbol.
- The number-line graph represents every value that makes the inequality true.
💡 Main Idea
To solve an inequality such as \( -5x+2>-13 \), isolate the variable using inverse operations. First subtract \(2\) from both sides, and then divide both sides by \(-5\). Because the division step involves a negative number, the inequality symbol must reverse direction. After solving, graph the solution on a number line to represent every possible value that satisfies the inequality.
🧠 Math Vocabulary
- Inequality: a mathematical statement that compares two quantities using symbols such as \( < \), \( > \), \( \le \), or \( \ge \).
- Solution: a value that makes an inequality true.
- Open Circle: shows that an endpoint is not included in the solution set.
- Inverse Operations: operations that undo one another and are used to isolate a variable.
- Reverse the Inequality: changing the direction of the inequality symbol after multiplying or dividing both sides by a negative number.
📚 What You Should Already Know
Students should know how to solve basic equations, use inverse operations, and interpret inequality symbols such as greater than, less than, greater than or equal to, and less than or equal to. They should also understand how values are represented on a number line.
🚀 What Comes Next
After solving one-step and two-step inequalities, students will move on to multi-step inequalities, compound inequalities, and inequalities with variables on both sides. These skills build toward solving real-world problems involving constraints and ranges of possible values.
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