Equition with absolute values

[lwebzem]

Hi,

I need to solve equiation |2x-1|=4x-7 by using real number line.

2x-1 is the distance between 1 and 2x. So I have on the real line number 2x.....1......2x
and 2x-1=4x-7 => x=3 (right side)
and 1-2x=4x-7 => x=8/6 (left side)

But 8/6 is not the correct solution. Why left side is giving not correct solution ? I expect it would give no solutions.
What I am doing wrong?

Thanks.

 

[stapel]

I don't know what is meant by "solving with a number line", so I'll just explain the algebra.

The argument in the absolute value, 2x - 1, is either negative or not. If it's non-negative, then |2x - 1| equals 2x - 1; that is, you can just drop the bars, just like for |3| = 3. If it's negative, then, just like you would change the sign for |-3| = -(-3) = +3, so also here. If 2x - 1 < 0, then |2x - 1| = -(2x - 1) = 1 - 2x.

So consider the two cases:

. . . . .2x - 1 < 0, so x < 1/2, and |2x - 1| = 1 - 2x:

. . . . .|2x - 1| = 4x - 7
. . . . .1 - 2x = 4x - 7
. . . . .8 = 6x
. . . . .8/6 = x = 4/3

. . . . .But 4/3 > 1/2, and x is supposed to be less than 1/2,
. . . . .so there is no solution in this case.

Now you consider the other case.

Eliz.