Let's break down the problems shown in the image:

Problem 6:

You are given points $A(-3)$ and $B(7)$ on a number line. If point $B$ moves 5 units to the left and reaches point $C$, you are asked to figure out how point $A$ must move to reach point $C$.

• Point $B(7)$ moves 5 units to the left: $C = 7 - 5 = 2$
• So, point $C$ is at $2$. Now, you need to find how point $A(-3)$ can move to reach point $C(2)$.
  • $A(-3)$ needs to move to the right by $2 - (-3) = 5$ units.

The correct answer is (C) Move 5 units to the right.

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Problem 7:

(1) $(-100) - (-78) + (-6)$:

This can be simplified step by step:

$(-100) - (-78) + (-6) = (-100 + 78) + (-6) = (-22) + (-6) = -28$

So, the answer is $-28$.

(2) $(-58) + (-272) - (-58)$:

Simplify the expression:

$(-58) + (-272) - (-58) = (-58) + (-272) + 58 = (-272)$

So, the answer is $-272$.

(3) $(-1200) - (378 - 1199)$:

First, simplify inside the parentheses:

$378 - 1199 = -821$ Now simplify the whole expression:

$(-1200) - (-821) = (-1200 + 821) = -379$

So, the answer is $-379$.

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Let me know if you need more details or have any questions! Here are 5 questions related to this topic:

1. What is the process of moving points along a number line?
2. How do you handle subtraction involving negative numbers?
3. How can you simplify expressions with multiple negative signs?
4. What is the general rule for adding and subtracting negative numbers?
5. How can number line movement problems be applied in geometry?

Tip: When subtracting a negative number, it's equivalent to adding its absolute value.