Diagnostic test questions for one-step subtraction inequalities

📚 Quick Study Guide

• 💡 Definition: An inequality that involves subtraction and can be solved in one step.
• 🔢 General Form: $x - a > b$, $x - a < b$, $x - a \geq b$, or $x - a \leq b$, where $x$ is the variable, and $a$ and $b$ are constants.
• ➕ Solving: To isolate $x$, add $a$ to both sides of the inequality. Remember that when adding or subtracting, the inequality sign does not flip.
• ⚖️ Example: Solve $x - 3 < 5$. Add 3 to both sides: $x - 3 + 3 < 5 + 3$, which simplifies to $x < 8$.
• 📈 Number Line: Represent the solution on a number line. Use an open circle for $<$ and $>$, and a closed circle for $\leq$ and $\geq$.
• ✔️ Checking: Substitute a value from your solution back into the original inequality to make sure it holds true.

Practice Quiz

1. What is the solution to the inequality $x - 5 > 3$?
   1. $x > -2$
   2. $x < 8$
   3. $x > 8$
   4. $x < -2$
2. Solve for $x$: $x - 2 \leq 7$
   1. $x \geq 9$
   2. $x \leq 5$
   3. $x \geq 5$
   4. $x \leq 9$
3. Which inequality represents: 'A number decreased by 4 is less than 10'?
   1. $x + 4 < 10$
   2. $x - 4 > 10$
   3. $x - 4 < 10$
   4. $x + 4 > 10$
4. What is the solution to $x - 1 \geq 6$?
   1. $x \geq 7$
   2. $x \leq 5$
   3. $x \leq 7$
   4. $x \geq 5$
5. Solve the inequality: $x - 8 < -2$
   1. $x < -10$
   2. $x > 6$
   3. $x < 6$
   4. $x > -10$
6. Which of the following values is a solution to the inequality $x - 3 \leq 1$?
   1. 5
   2. 6
   3. 4
   4. 7
7. What is the solution set for $x - 6 > -1$?
   1. $x > -7$
   2. $x < 5$
   3. $x > 5$
   4. $x < -7$