Example Problems: One-Step Inequality Word Problems with Detailed Solutions

📚 Quick Study Guide

• ➕ Addition Property: If $a > b$, then $a + c > b + c$
• ➖ Subtraction Property: If $a > b$, then $a - c > b - c$
• ✖️ Multiplication Property (Positive): If $a > b$ and $c > 0$, then $ac > bc$
• ➗ Division Property (Positive): If $a > b$ and $c > 0$, then $\frac{a}{c} > \frac{b}{c}$
• ✖️ Multiplication Property (Negative): If $a > b$ and $c < 0$, then $ac < bc$ (reverse the inequality)
• ➗ Division Property (Negative): If $a > b$ and $c < 0$, then $\frac{a}{c} < \frac{b}{c}$ (reverse the inequality)
• ✍️ Keywords: "More than" ($>$), "Less than" ($<$), "At least" ($\geq$), "At most" ($\leq$)

🤔 Practice Quiz

1. What inequality represents: "A number $x$ plus 5 is greater than 10"?
   1. $x + 5 < 10$
   2. $x + 5 > 10$
   3. $x - 5 > 10$
   4. $x - 5 < 10$
2. John wants to save more than $50. He has already saved $20. How much more does he need to save? Let $x$ be the amount he still needs to save.
   1. $x + 20 < 50$
   2. $x + 20 > 50$
   3. $x - 20 > 50$
   4. $x - 20 < 50$
3. Which inequality represents: "Twice a number $y$ is at most 12"?
   1. $2y < 12$
   2. $2y > 12$
   3. $2y \leq 12$
   4. $2y \geq 12$
4. Sarah wants to spend less than $30 on groceries. She already has $12 worth of items. How much more can she spend? Let $g$ be the additional amount she can spend.
   1. $g + 12 > 30$
   2. $g + 12 < 30$
   3. $g - 12 < 30$
   4. $g - 12 > 30$
5. What is the solution to the inequality $x - 3 > 7$?
   1. $x < 10$
   2. $x > 10$
   3. $x < 4$
   4. $x > 4$
6. Solve the inequality: $\frac{y}{2} \leq 5$
   1. $y \geq 10$
   2. $y \leq 10$
   3. $y \geq \frac{5}{2}$
   4. $y \leq \frac{5}{2}$
7. A store requires you to be at least 16 years old to work there. If $a$ represents an applicant's age, which inequality shows who they will hire?
   1. $a < 16$
   2. $a > 16$
   3. $a \leq 16$
   4. $a \geq 16$