📚 Topic Summary
Linear inequalities are mathematical statements that compare two expressions using inequality symbols such as $<$, $>$, $\leq$, or $\geq$. Unlike equations, which have one specific solution, inequalities have a range of solutions. In real-world scenarios, linear inequalities help us model situations where there are constraints or limits, such as budget limitations, minimum requirements, or capacity restrictions. They allow us to determine all possible values that satisfy a given condition. Solving these inequalities provides valuable insights for making informed decisions.
🧠 Part A: Vocabulary
Match each term with its definition:
- Term: Inequality Symbol
- Term: Solution Set
- Term: Constraint
- Term: Variable
- Term: Linear Inequality
- Definition: A letter representing an unknown value.
- Definition: A limit or restriction in a real-world problem.
- Definition: A symbol such as $<$, $>$, $\leq$, or $\geq$ used to compare values.
- Definition: The set of all values that satisfy an inequality.
- Definition: A mathematical statement that compares two expressions using an inequality symbol.
✏️ Part B: Fill in the Blanks
Linear ________ are used to represent real-world situations where quantities are not necessarily ________. These inequalities involve variables and ________ that express relationships like “less than” or “greater than.” For example, if you have a budget of $\$50$ for groceries, and you want to buy apples that cost $\$2$ each, the inequality $2x \leq 50$ can represent the ________ on the number of apples ($x$) you can buy.
🤔 Part C: Critical Thinking
Describe a real-world situation (different from the grocery example) where using a linear inequality would be helpful in making a decision. Explain what the variable would represent and what the inequality would model.