๐ Quick Study Guide
โ Linear inequalities are mathematical statements that compare two expressions using inequality symbols such as $<$, $>$, $\leq$, or $\geq$.
๐ก Translating verbal statements into linear inequalities involves identifying key phrases that indicate inequality, such as "at least," "no more than," "less than," or "greater than."
โ๏ธ Steps to translate: 1) Define the variable, 2) Identify inequality keywords, 3) Write the inequality.
โ Solving linear inequalities is similar to solving linear equations, but with one key difference: multiplying or dividing by a negative number reverses the inequality sign.
๐ Real-world applications include budgeting, resource allocation, and setting constraints.
Practice Quiz
1. Sarah wants to save at least $500. She has already saved $200. Which inequality represents how much more she needs to save, $x$?
A. $x < 300$
B. $x > 300$
C. $x \leq 300$
D. $x \geq 300$
2. A school allows no more than 30 students per class. Let $s$ be the number of students in a class. Which inequality represents this situation?
A. $s > 30$
B. $s < 30$
C. $s \geq 30$
D. $s \leq 30$
3. John wants to spend less than $20 on lunch. He orders a drink for $3. Which inequality represents how much he can spend on his meal, $m$?
A. $m > 17$
B. $m < 17$
C. $m \geq 17$
D. $m \leq 17$
4. To qualify for a race, runners must complete the course in under 60 minutes. Let $t$ be the time it takes a runner to complete the course. Which inequality represents this?
A. $t \geq 60$
B. $t \leq 60$
C. $t > 60$
D. $t < 60$
5. A company needs to produce at least 1000 units of a product. They have already produced 300 units. Let $x$ represent the number of units left to produce. Which inequality represents this situation?
A. $x \leq 700$
B. $x \geq 700$
C. $x < 700$
D. $x > 700$
6. A store requires customers to be at least 16 years old to purchase certain items. Let $a$ be the age of a customer. Which inequality represents this requirement?
A. $a < 16$
B. $a > 16$
C. $a \leq 16$
D. $a \geq 16$
7. A movie theater can hold a maximum of 250 people. Let $p$ be the number of people in the theater. Which inequality represents this?
A. $p > 250$
B. $p < 250$
C. $p \geq 250$
D. $p \leq 250$
Click to see Answers
- D
- D
- B
- D
- B
- D
- D