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12 Jan 2017, 21:14
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Hi, I am looking for some clarity on when we CAN and CANNOT divide by a variable. 
Scenario 1:
x^2 = 10x
x^2/x = 10x/x would be incorrect.
We would need to solve this as follows:
x^2 - 10x = 0
x(x - 10) = 0
x=0 or x=10
Scenario 2:
y = 4x
y/x = 4x/x
y/x = 4
Why is it that we cannot divide by x in scenario 1, but we can divide by x in scenario 2?
Thank you for your help.
Scenario 1:
x^2 = 10x
x^2/x = 10x/x would be incorrect.
We would need to solve this as follows:
x^2 - 10x = 0
x(x - 10) = 0
x=0 or x=10
Scenario 2:
y = 4x
y/x = 4x/x
y/x = 4
Why is it that we cannot divide by x in scenario 1, but we can divide by x in scenario 2?
Thank you for your help.
12 Jan 2017, 23:08
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Hi CoolFool,
You have to be careful when dividing by a variable (because you might inadvertently remove a potential solution from the equation that you're manipulating). As you've already noticed, in your first example - by diving both sides by X - you REMOVED a variable (and thus, you removed a solution). However, in your second example, by dividing by X, you did NOT remove it (you simply 'moved' it to the other side of the equation) - so that's mathematically acceptable.
GMAT assassins aren't born, they're made,
Rich
You have to be careful when dividing by a variable (because you might inadvertently remove a potential solution from the equation that you're manipulating). As you've already noticed, in your first example - by diving both sides by X - you REMOVED a variable (and thus, you removed a solution). However, in your second example, by dividing by X, you did NOT remove it (you simply 'moved' it to the other side of the equation) - so that's mathematically acceptable.
GMAT assassins aren't born, they're made,
Rich
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13 Jan 2017, 07:44
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the problem with the variables is that they can be either zero or negative. A negative number, raised to an even exponent, will yield a positive number. From here, the confusion might arise. Every time when you solve a question, ask yourself - can the exponent be zero or negative? Moreover, when you deal with an expression that has exponents >1, you need to realize that you might have more than one solution for the variable.
