Solved Examples: One-Step Inequalities Using Addition Properties

📚 Quick Study Guide

🔢 Inequality Basics: Inequalities use symbols like < (less than), > (greater than), $\leq$ (less than or equal to), and $\geq$ (greater than or equal to) to show relationships between values. ➕ Addition Property of Inequality: Adding the same number to both sides of an inequality does not change the inequality's direction. If $a > b$, then $a + c > b + c$. ➖ Subtraction Property of Inequality (for solving with addition): Similar to addition, subtracting the same number from both sides doesn't change the inequality. If $a < b$, then $a - c < b - c$. 💡 Solving One-Step Inequalities: Isolate the variable by using the inverse operation (addition or subtraction) on both sides of the inequality. 📈 Graphing Inequalities: Use a number line to represent the solutions. Open circles indicate $<$ or $>$, while closed circles indicate $\leq$ or $\geq$.

✏️ Practice Quiz

1. What is the solution to the inequality $x - 3 > 5$?
   1. $x > 2$
   2. $x < 2$
   3. $x > 8$
   4. $x < 8$
2. Solve the inequality: $y - 7 \leq 2$
   1. $y \leq 9$
   2. $y \geq 9$
   3. $y \leq -5$
   4. $y \geq -5$
3. What is the solution to $z + 4 < 10$?
   1. $z < 6$
   2. $z > 6$
   3. $z < 14$
   4. $z > 14$
4. Solve: $a + 2 \geq -3$
   1. $a \geq -5$
   2. $a \leq -5$
   3. $a \geq 5$
   4. $a \leq 5$
5. Find the solution to $b - 1 > -4$
   1. $b > -5$
   2. $b > -3$
   3. $b < -5$
   4. $b < -3$
6. What is the solution set for $c + 6 \leq 1$?
   1. $c \leq -5$
   2. $c \geq -5$
   3. $c \leq 7$
   4. $c \geq 7$
7. Solve the inequality: $d - 5 \geq -10$
   1. $d \geq -5$
   2. $d \leq -5$
   3. $d \geq 15$
   4. $d \leq 15$