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April 24, 2014

Homework Help: math

Posted by jasmine20 on Monday, January 1, 2007 at 4:44am.

can someone correct this for me...
solve:
-4(2x - 3) = -8x + 5

my answer:
this equation has no solution because they don't equal

i get 0=-7

-4(2x-3)=-8x+5

-8x+12=-8x+5

0(x)=-7

So am I correct

You are right, let me explain a bit more.

When you write down:

-4(2x - 3) = -8x + 5

you actually say: Suppose there exists an x such that
-4(2x - 3) equals -8x + 5

Then, assuming this is true, you attempt to find, using some manipulations ,the value of x. If you find a value for x, then you should still check if the equation is satisfied, although this last step is often skipped.

But in this case you find a contradictory statement:

0 = -7

This statement is false, which means that the orginal assumption that there exists an x such that
-4(2x - 3) equals -8x + 5
must be false.

To see this let's take statement A to be: "There exists an x such that
-4(2x - 3) equals -8x + 5"

And let's take statement B to be:
"0 = -7". Let's forget for a minute that statement B is obviously false.

Using Algebra you have shown that if A is true then B must be true. In such a case you can also conclude that if B is not true, then A must be false. So, if you know B to be false, then you know that A must be false because if A were true then B must be true which you know isn't the case.

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