1. **Problem:** Determine which statements about inequalities are true. - A. $3 < -3$ - B. $4 > -4$ - C. $-2 > 0$ - D. $-8 > -5$ **Step:** Recall that positive numbers are always greater than negative numbers, and on the number line, numbers increase from left to right. - $3 < -3$ is false because 3 is positive and -3 is negative. - $4 > -4$ is true because 4 is positive and greater than -4. - $-2 > 0$ is false because -2 is negative. - $-8 > -5$ is false because -8 is less than -5. **Answer:** B is correct. 2. **Problem:** Calculate $3 + (-5) - 6$. **Step:** Use the order of operations and combine terms step-by-step. $$3 + (-5) - 6 = (3 - 5) - 6 = -2 - 6 = -8$$ **Answer:** C. -8 3. **Problem:** Identify the value of point B on the number line. **Step:** From the description, point B is at 3. **Answer:** B. 3 4. **Problem:** Determine which statement about negation and addition is true. - A. $-(5 - 7 + 1) = -5 - 7 + 1$ - B. $- (-7 + 8 - 13) = 7 - 8 + 13$ - C. $+ (7 - 15 + 12) = 7 + 15 + 12$ - D. $- (-4 + 16 - 25) = -4 - 16 + 25$ **Step:** Apply the distributive property of negation: - $-(a + b + c) = -a - b - c$ - $-(-a + b - c) = a - b + c$ Check each: - A: $-(5 - 7 + 1) = -5 + 7 - 1$ which is not equal to $-5 - 7 + 1$ - B: $-(-7 + 8 - 13) = 7 - 8 + 13$ correct - C: $+(7 - 15 + 12) = 7 - 15 + 12$ not $7 + 15 + 12$ - D: $-(-4 + 16 - 25) = 4 - 16 + 25$ not $-4 - 16 + 25$ **Answer:** B is correct. 5. **Problem:** A person starts at 0 on the number line, moves 4 units right to +4, then 4 units left. Where do they stop? **Step:** Starting at 0, moving right 4 units lands at 4. Moving left 4 units from 4: $$4 - 4 = 0$$ **Answer:** The person stops at 0.