3x+1/10=x-1/7 what is x explain how you got the answer do a step by step solution

Ok, to solve an algebraic equation we need to get the unknown by itself on one side of the equals sign.  To do that, basically we just have to cancel everything else out... but whatever we do to cancel out what we don't want, we also have to do on the other side of the equals sign...

3x + 1/10 = x - 1/7

Let's start by getting the x on the right over to the left side.  To cancel it from the right side we have to subtract it (x-x = 0).  Don't forget to subtract it on the left also.

3x -x + 1/10 = x - x - 1/7

Now combine like terms

2x + 1/10 = -1/7

Now let's bring the 1/10 over to the right of the equals sign to get x by itself by subtracting it.

2x + 1/10 - 1/10 = -1/7 - 1/10
 
Combine like terms

2x = -1/7 - 1/10

Let's get a common denominator so we can combine the fractions

2x = -10/70 - 7/70
2x = -17/70

Now divide both sides by 2 to finish getting x by itself.  To divide fractions, multiply the reciprocal.

x = -17/70 x 1/2
x = -17/140