Absolute Value Equation

I normally know how to do these but for some reason can't find my error when doing the problem, 5|3x-4|=x+1
Here are my steps to get the positve case:
|3x-4|=x/5+1/5 divided each side by 5

(3x-4=x/5+1/5)5 multiplyed everything by 5 to get rid of fractions

15x-20=x+1

14x-20=1 subtracted x from each side

14x=21

I get x=3/2 and the right answer is 3/5, can someone point out where i went wrong?

You start with "x + 1/5", and, after dividing everything by 5, have "x/5 + 1/5". Shouldn't that be "x/5 + 1/25"?

Also, on what basis did you remove the absolute-value bars as though they were parentheses? Aren't you supposed to split the equation into two cases, solving each? For instance:

. . . . .|x| = 3

. . . . .x = 3 or x = -3

Eliz.

Absolute Value equation

First i made a mistake when typing it up, the original equation should be 5|3x-4|=x+1, and i removed the absolute value bars because when you are solving for both cases you remove the bars and solve the two cases just as regular equations, this was how i was taught. For the negative case i got 19/16, which is right, now i just need someone to show me where i went wrong with the positve case now that i have corrected the mistake.

I don't see the point of dividing through by five, just to multiply through by five. Nothing changes.

Meanwhile, if the equation is 5|3x - 4| = x + (1/5), I'm not seeing how you can convert this to 5|3x - 4| = x + 1. What happened to the "one-fifth"?

Eliz.

Absolute value equation

The 1/5 was a mistake made by me when i typed up the post. There was never a 1/5 in the original problem. The problem was 5|3x-4|=x+1. I am still wanting some one to tell me the mistake i made. The right answer is 3/5.

Checking:

. . . . .x = 3/5:

. . . . .5|3x - 4| = x + 1
. . . . .5|3(3/5) - 4| ?=? (3/5) + 1
. . . . .5|9/5 - 20/5| ?=? 8/5
. . . . .5|-11/5| ?=? 8/5
. . . . .5(11/5) ?=? 8/5
. . . . .11 ?=? 8/5

Since 11 does not equal 8/5, then "x = 3/5" cannot be a solution.

Checking your solution:

. . . . .x = 3/2:

. . . . .5|3x - 4| = x + 1
. . . . .5|3(3/2) - 4| ?=? (3/2) + 1
. . . . .5|9/2 - 8/2| ?=? 5/2
. . . . .5|1/2| ?=? 5/2
. . . . .5(1/2) ?=? 5/2
. . . . .5/2 ?=? 5/2

Since 5/2 = 5/2, your solution is correct. Whoever told you that the solution was 3/5 was mistaken. Sorry.

Eliz.