Thursday, September 19, 2013

Do the equations x = 4y + 1 and x = 4y – 1 have the same solution? How might you explain your answer to someone who has not learned algebra?

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They do not have the same solution simply because you can’t add and subtract a number from the same equation and get the same number. It just doesn’t work, especially in a line graph. If I was to explain this to someone who didn’t know what algebra was I would first take away the x value and just leave it blank. I would then assign a number to y, like 3. I would multiply it out, and show them that when 4y+1 = 13 it is not the same answer as when 4y-1 = 11. This would probably be the easiest way to explain that adding and subtracting that same number isn’t going to give you a similar value. If they still didn’t understand what I meant by the explanation I have used, I would then substitute 4 in for the 4y. I would ask them if 4+1 is the same as 4-1. I would illustrate perhaps by saying would you like 4 dollars plus 1 dollar or 4 dollars minus 1 dollar. Any logical person will choose to take the 4+1 dollars and more simply understand that the x value represented in the equation is just the answer after adding or subtracting the 1.

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