Can Someone help me solve these two problems
Absolute value of 2x+1 = x-1 (two solutions i think?)
and
square root of 3x+1 = 3 + square root of x-4
please help me solve
In order to solve an absolute value problem, you have to solve two separate equations. The first will be and the second will be or equivalently, .
For the square root problem you begin with . What you need to do is square both sides, then put everything that's not under a square root on one side, and square both sides again.
You can pull the one out since it is always positive:
From here it should be clear that, as you have already discovered, there are no solutions, because no matter the value of x, |2x| will always be greater than it, and so |2x|-x will always be greater than or equal to zero, and thus can never equal -2.
Be sure to see that the method that icemanfan showed you still works; you just have to be careful about your signs:
Considering the two cases separately:
, but this contradicts our requirement that so it is not a solution.
, but this contradicts our requirement that so it is also not a solution.
These are the only two possibilities (from the trichotomy law), so the original equation has no solutions.
It is, however, always a good idea to check your values in the original equation, because unless you are very careful in performing operations you can easily end up with extraneous (and sometimes missing) solutions.