math
posted by jasmine20
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(2x3)=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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