Test questions for identifying inequality solutions Grade 7

📚 Quick Study Guide

🔢 Understanding Inequalities: Inequalities compare two values, showing that they are not simply equal. We use symbols like < (less than), > (greater than), $\leq$ (less than or equal to), and $\geq$ (greater than or equal to). 💡 Solving Inequalities: Solving inequalities is similar to solving equations, but with one key difference: when you multiply or divide both sides by a negative number, you must flip the inequality sign. ⚖️ Representing Solutions: Solutions to inequalities can be represented on a number line. An open circle indicates that the endpoint is not included (for < and >), while a closed circle indicates that it is included (for $\leq$ and $\geq$). 📝 Writing Solutions: The solution to an inequality is a range of values. For example, $x > 3$ means x can be any number greater than 3. ➕ Adding/Subtracting: Adding or subtracting the same number from both sides of an inequality doesn't change the inequality. ➗ Multiplying/Dividing by Positive Numbers: Multiplying or dividing both sides by the same positive number doesn't change the inequality. ➖ Multiplying/Dividing by Negative Numbers: Multiplying or dividing both sides by the same negative number *reverses* the inequality.

🧪 Practice Quiz

1. What is the solution to the inequality $x + 5 < 12$?
   1. $x < 7$
   2. $x > 7$
   3. $x < 17$
   4. $x > 17$
2. Solve for $y$: $3y \geq 15$
   1. $y \geq 5$
   2. $y \leq 5$
   3. $y \geq 45$
   4. $y \leq 45$
3. Which inequality is represented by the number line showing a closed circle at -2 and shading to the left?
   1. $x > -2$
   2. $x < -2$
   3. $x \geq -2$
   4. $x \leq -2$
4. Solve: $-2z < 10$
   1. $z < -5$
   2. $z > -5$
   3. $z < 5$
   4. $z > 5$
5. What is the solution set for $2a - 3 \leq 7$?
   1. $a \leq 5$
   2. $a \geq 5$
   3. $a \leq 2$
   4. $a \geq 2$
6. Solve the inequality: $\frac{b}{4} > 2$
   1. $b > 8$
   2. $b < 8$
   3. $b > \frac{1}{2}$
   4. $b < \frac{1}{2}$
7. Which of the following values of $p$ satisfies the inequality $5p + 2 > 17$?
   1. $p = 2$
   2. $p = 3$
   3. $p = 4$
   4. $p = 1$