by **RonPurewal** Fri Jan 29, 2010 8:28 am

the above posts are making my eyes hurt, because i'm lazy and don't like solutions with lots of steps.

also, there's no way that most people are going to be able to execute all those steps within the requisite time. (remember that this is just one statement, not even the whole problem!)

here's a takeaway that should help you ladies and gentlemen:

if you get

| QUANTITY1 | = QUANTITY2

or

| QUANTITY1 | = | QUANTITY2 |

then just

solve the following two equations:

QUANTITY1 = QUANTITY2

QUANTITY1 = -(QUANTITY2)

and then

CHECK your solutions, in the ORIGINAL EQUATION.

that's it, folks. no worrying about "areas of interest" or signs in bars. none of that.

just solve the two equations above, and check.

advanced:

if the equation has absolute values on both sides (i.e., |quantity1| = |quantity2| ), then you don't even have to check the solutions. they will ALWAYS work.

...but it's easier on your memory just to check them all the time - it only takes a few seconds - rather than to worry about when you have to check and when you don't.

--

so, for statement 2:

just solve

x = 3x - 2

and

x = -(3x - 2)

the solution to the former is 1. the solution to the latter is 1/2.

now, check the answers IN THE ORIGINAL EQUATION.

1 works.

1/2 does not work (the left side is positive; the right side is negative).

so, x = 1.

for once, it really is that simple!

refreshing, in a sea of problems that tend to be less simple than they appear.