Solved examples: applying properties of inequality grade 7.

📚 Quick Study Guide

🔍 Understanding Inequalities: Inequalities compare values that are not necessarily equal. We use symbols like < (less than), > (greater than), $\leq$ (less than or equal to), and $\geq$ (greater than or equal to).

➕ Addition Property: Adding the same number to both sides of an inequality does not change the inequality. If $a < b$, then $a + c < b + c$.

➖ Subtraction Property: Subtracting the same number from both sides of an inequality does not change the inequality. If $a > b$, then $a - c > b - c$.

✖️ Multiplication Property (Positive Number): Multiplying both sides of an inequality by a positive number does not change the inequality. If $a < b$ and $c > 0$, then $ac < bc$.

➗ Division Property (Positive Number): Dividing both sides of an inequality by a positive number does not change the inequality. If $a > b$ and $c > 0$, then $\frac{a}{c} > \frac{b}{c}$.

🔄 Multiplication Property (Negative Number): Multiplying both sides of an inequality by a negative number reverses the inequality sign. If $a < b$ and $c < 0$, then $ac > bc$.

➗ Division Property (Negative Number): Dividing both sides of an inequality by a negative number reverses the inequality sign. If $a > b$ and $c < 0$, then $\frac{a}{c} < \frac{b}{c}$.

Practice Quiz

1. What is the solution to the inequality $x + 3 < 7$?
1. $x < 4$
2. $x > 4$
3. $x < 10$
4. $x > 10$
2. Solve the inequality $y - 5 > 2$.
1. $y > 7$
2. $y < 7$
3. $y > -3$
4. $y < -3$
3. What is the solution to $2z \leq 8$?
1. $z \leq 4$
2. $z \geq 4$
3. $z \leq 16$
4. $z \geq 16$
4. Solve the inequality $\frac{w}{3} > 1$.
1. $w > 3$
2. $w < 3$
3. $w > \frac{1}{3}$
4. $w < \frac{1}{3}$
5. If $-a > 5$, then which of the following is true?
1. $a < -5$
2. $a > -5$
3. $a < 5$
4. $a > 5$
6. Solve $-3b \leq 9$.
1. $b \geq -3$
2. $b \leq -3$
3. $b \geq 3$
4. $b \leq 3$
7. Which inequality is equivalent to $4c - 2 < 10$?
1. $c < 3$
2. $c > 3$
3. $c < 2$
4. $c > 2$