🔑 Key Concepts
- Combine like terms first if the variable appears more than once on one side of the inequality.
- Solve inequalities using inverse operations just like equations.
- When dividing or multiplying by a negative number, the inequality symbol reverses.
- After solving, graph the solution on a number line using an open or closed circle.
- An open circle means the endpoint is not included, and a closed circle means it is included.
🧠 Math Vocabulary
- Combine Like Terms: simplify terms with the same variable part.
- Inequality: a mathematical statement using symbols such as \( < \), \( > \), \( \le \), or \( \ge \).
- Open Circle: the endpoint is not included in the solution.
- Closed Circle: the endpoint is included in the solution.
- Reverse the Inequality: when multiplying or dividing by a negative number, the symbol changes direction.
💡 Main Idea
To solve and graph an inequality like the ones in this lesson, first simplify each side by combining like terms. Then isolate the variable using inverse operations. If you divide by a negative number, the inequality symbol must reverse. After solving, graph the solution on a number line using an open circle when the endpoint is not included and a closed circle when it is included.
📚 What You Should Already Know
Students should already understand one-step equations, integer operations, and how to interpret inequality symbols. It also helps to know how to combine like terms before solving.
🚀 What Comes Next
After solving and graphing one-variable inequalities, students can move on to multi-step inequalities, inequalities with variables on both sides, and writing inequalities from verbal statements and real-world situations.
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