📝 Practice Worksheets
🛠️ Related Tool
Inequality Graphing Explorer🔑 Key Concepts
- You can clear a fraction by multiplying both sides by the denominator.
- After simplifying, combine like terms and isolate the variable.
- When dividing by a negative number, reverse the inequality symbol.
- A closed circle means the endpoint is included in the solution.
- A graph on the number line shows all values that make the inequality true.
🧠 Math Vocabulary
- Inequality: A math sentence that compares two expressions using symbols such as \( \lt \), \( \gt \), \( \le \), or \( \ge \).
- Closed circle: A point on the number line showing the endpoint is included in the solution.
- Open circle: A point on the number line showing the endpoint is not included in the solution.
- Reverse the inequality: When dividing by a negative number, the inequality symbol must change direction.
- Solution set: All values that make the inequality true.
💡 Main Idea
Some inequalities require clearing fractions before isolating the variable. After simplifying, solving follows the same process as equations, except that dividing by a negative number reverses the inequality symbol. Once solved, the solution can be graphed on a number line to show all values that work.
📚 What You Should Already Know
Before working on these problems, students should be comfortable with inverse operations, multiplying both sides of an equation by the same number, combining like terms, and reading a number line. Students should also understand that negative values can change the direction of an inequality when dividing.
🚀 What Comes Next
After solving and graphing one-variable inequalities involving negatives and fractions, students are ready for compound inequalities, word problems with inequality constraints, and later systems of inequalities on the coordinate plane.
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