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(question 1)
What must be added to 5X+7Y-19Z to get 7X-7Y-15Z?
Let W be the answer. Then
5X+7Y-19Z PLUS W MUST EQUAL 7X-7Y-15Z
ß ß ß ß ß
5X+7Y-19Z + W = 7X-7Y-15Z
5X + 7Y - 19Z + W = 7X - 7Y - 15Z
Add -5X to both sides
5X + 7Y - 19Z + W = 7X - 7Y - 15Z
-5X -5X
------------------------------------
7Y - 19Z + W = 2X - 7Y - 15Z
Add -7Y to both sides
7Y - 19Z + W = 2X - 7Y - 15Z
-7Y -7Y
--------------------------------
-19Z + W = 2X - 14Y - 15Z
-19Z + W = 2X - 14Y - 15Z
Add +19Z to both sides
-19Z + W = 2X - 14Y - 15Z
+19Z + 19Z
-----------------------------
W = 2X - 14Y + 4Z
So the answer is 2X - 14Y + 4Z
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(question 2)
What must be subtracted from 3A+4B²-5C to give 2A+3B²+5C
Let W be the answer. Then
3A+4B²-5C MINUS W MUST EQUAL 2A+3B²+5C
ß ß ß ß ß
3A+4B²-5C - W = 2A+3B²+5C
3A + 4B² - 5C - W = 2A + 3B² + 5C
Add -3A to both sides
3A + 4B² - 5C - W = 2A + 3B² + 5C
-3A -3A
---------------------------------------
4B² - 5C - W = -A + 3B² + 5C
Add -4B² to both sides
4B² - 5C - W = -A + 3B² + 5C
-4B² -4B²
---------------------------------
-5C - W = -A - B² + 5C
Add +5C to both sides:
-5C - W = -A - B² + 5C
+5C +5C
----------------------------
-W = -A - B² + 10C
We want W not -W, so we multiply both sides by -1
-1(-W) = -1(-A - B² + 10C)
W = A + B² - 10C
So the answer is A + B² - 10
Edwin
