Writing Inequalities from Word Problems — Understanding Maximum and Capacity

🔑 Key Concepts

  • Words like maximum, capacity, or limit usually mean the value cannot go over a certain number.
  • A maximum or capacity is represented using the symbol \(\le\).
  • Translate real-world situations into mathematical inequalities using a variable.
  • Always identify the quantity being limited before writing the inequality.
  • Check whether the value can equal the limit or must stay strictly below it.

✏️ Worked Examples — Understanding Limits and Capacity

🧠 Math Vocabulary

  • Maximum: The greatest value allowed. In math, this usually means the quantity must be less than or equal to a number, written as \(\le\).
  • Capacity: The largest amount something can hold without exceeding a limit.
  • Limit: A boundary that cannot be passed. The value may reach the limit, but it cannot go beyond it.
  • Inequality: A mathematical statement that compares two quantities using symbols such as \(<\), \(>\), \(\le\), or \(\ge\).
  • Variable: A letter used to represent an unknown quantity.

💡 Main Idea

When a situation describes a maximum, capacity, or limit, it means the value can go up to a certain number but cannot go over it. In mathematics, we represent this idea using the symbol \(\le\). Writing inequalities helps us model real-world limits and understand how much can safely be added or allowed.

📚 What You Should Already Know

Before writing inequalities from word problems, you should understand how to use variables to represent unknown quantities and recognize basic inequality symbols such as \(<\), \(>\), \(\le\), and \(\ge\). You should also be comfortable interpreting real-world quantities such as weight, speed, and number of people.

🚀 What Comes Next

After learning how to write inequalities from verbal statements, the next step is solving inequalities and graphing the solutions on a number line. You will also apply inequalities to more complex real-world situations involving budgets, measurements, and safety limits.

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