If x divided by 67 then log56 after you fivide it by 1222 then what will happen if x changes its distribiton from 6 to 9
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Answer:
During math problems on the GMAT, test-takers might see problems like these:
x3 - 4x2 + 4x = 0
Does (3x)/(7x) equal 3/7?
For what values does [(x+3)(x-5)]/[(x+3)(x-6)] equal (x-5)/(x-6)?
It can be tempting to divide by x in these problems to get simpler equations, but this is not a correct strategy.
Why Can’t You Divide by X?
One essential rule in algebra is that dividing by 0 is undefined. It’s easy to see this in an example, like 10/0. What does this mean? The fraction stands for 10 ÷ 0, which tells us to cut 10 into 0 equal parts—that’s not possible. Since multiplication “undoes” division, look at the problem this way: what number times 0 gives back 10? Nothing!
The practice problems above have x terms instead of 0, so it might seem all right at first to divide by x and reduce these problems. However, we don’t know what number x represents, so we can’t divide by x in case it stands for 0.
How Can We Solve The Equations on the GMAT?
If we can’t divide by x, there must be another way to approach these problems. Let’s look at the first question again.
x3 - 4x2 + 4x = 0
We can’t divide both sides by x, but we can factor the left side.
x(x2 - 4x + 4) =
Now we know that x times (x2 - 4x + 4) equals 0, which means either x = 0 or (x2 - 4x + 4) = 0. If (x2 - 4x + 4) = 0, we’ll factor the quadratic equation to (x-2)(x-2) = 0. Now x = 0 or (x-2) = 0, which reduces to x=2. The only answer choices for x are 0 and 2.
Avoiding a Division Trap
The second problem shows an equation that looks easy to solve. Take a close look.
Does (3x)/(7x) equal 3/7?
If you plug in a few numbers, it looks like the equation holds.
(3*5)/(7*5) = 3/7 and (3*2)/(7*2) = 3/7
Without taking a moment to think, it seems like this equation is true. But what happens if x = 0? Then our fraction is undefined and we get 0 on top and 0 on bottom. Now it’s clear that the equation is true unless x = 0.