Solved examples of one-step subtraction inequalities

📚 Quick Study Guide

🔍 Inequality Symbols:
• $>$: Greater than
• $<$: Less than
• $\geq$: Greater than or equal to
• $\leq$: Less than or equal to

💡 Solving One-Step Subtraction Inequalities:
• Isolate the variable by performing the inverse operation (addition) on both sides of the inequality.
• If you multiply or divide by a negative number, remember to flip the inequality sign.

📝 Example:
• Solve for $x$: $x - 3 > 5$
• Add 3 to both sides: $x - 3 + 3 > 5 + 3$
• Simplify: $x > 8$

Practice Quiz

1. What is the solution to the inequality $x - 5 < 3$?
1. $x < 8$
2. $x > 8$
3. $x < -2$
4. $x > -2$


2. Solve the inequality $y - 2 \geq 10$.
1. $y \geq 12$
2. $y \leq 12$
3. $y \geq 8$
4. $y \leq 8$


3. Which of the following is the correct solution for $z - 7 > -1$?
1. $z > 6$
2. $z < 6$
3. $z > -8$
4. $z < -8$


4. Find the solution to the inequality $a - 4 \leq 0$.
1. $a \leq 4$
2. $a \geq 4$
3. $a \leq -4$
4. $a \geq -4$


5. What is the solution set for the inequality $b - 1 > 9$?
1. $b > 10$
2. $b < 10$
3. $b > 8$
4. $b < 8$


6. Solve the inequality $c - 6 \geq -2$.
1. $c \geq 4$
2. $c \leq 4$
3. $c \geq -8$
4. $c \leq -8$


7. Which inequality is satisfied by $d = 5$ given the inequality $d-2 < x$?
1. $x>3$
2. $x<3$
3. $x>7$
4. $x<7$