Solving Multi-Step Inequalities

🔑 Key Concepts

  • Use the distributive property before combining like terms.
  • Combine like terms on each side to simplify the inequality.
  • Perform the same operation on both sides to keep the inequality balanced.
  • If you multiply or divide both sides by a negative number, reverse the inequality sign.
  • Write the solution clearly using an inequality statement.

✏️ Worked Examples — Solving Multi-Step Inequalities

🧠 Math Vocabulary

  • Inequality: A mathematical statement that compares two quantities using symbols such as \( < \), \( > \), \( \le \), or \( \ge \).
  • Distributive Property: Multiplying a number by each term inside parentheses.
  • Like Terms: Terms that have the same variable part and can be combined.
  • Inverse Operations: Operations that undo each other, such as addition and subtraction or multiplication and division.
  • Solution: Any value that makes the inequality true.

💡 Main Idea

Solving a multi-step inequality is a lot like solving a multi-step equation. First, simplify each side by distributing and combining like terms. Then use inverse operations to isolate the variable. The most important difference is that if you multiply or divide both sides by a negative number, you must reverse the direction of the inequality sign.

📚 What You Should Already Know

Before working with multi-step inequalities, you should be comfortable using the distributive property, combining like terms, and solving basic one-step and two-step equations. It also helps to understand that whatever operation is done to one side must also be done to the other side to keep the statement balanced.

🚀 What Comes Next

After solving multi-step inequalities algebraically, the next step is to graph the solutions on a number line and interpret what the inequality means visually. From there, you can move into compound inequalities and applications involving real-world situations.

🧩 Embed This Video in Your LMS

Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.