Hello! Maybe someone has some time to help me?
So, with which values of "a" equatation of "ax+2=x" solution is less than 3?

Question

Hello! Maybe someone has some time to help me?
So, with which values of "a" equatation of "ax+2=x" solution is less than 3?

tamtoan · Answer

subtract x both side then subtract 2 both side again...what do you get?

kamille · Answer

ax+2=x-x
ax+2-x=0
ax-x=-2

kamille · Answer

Whats next?:s

tamtoan · Answer

now factore the x out on the left side and divide the factor to separate x

kamille · Answer

x(a-2)=-2?

kamille · Answer

Can you show me?

tamtoan · Answer

ok divide a-2 to both side of equation

tamtoan · Answer

what do you get now ?

kamille · Answer

I don't need to find x, I need to find values of a. 
But x=-2(a-2)

tamtoan · Answer

no, if you divide both side by a-2  ...you have x = -2/(a-2) ...and since your solution x is less than 3...                  x  < 3   which is the same as
                         -2/(a-2)   < 3   can you solve for a from here?

kamille · Answer

-2/(a-2)<3
-2-3a+6/a-2<0
-3a+4/(a-2)<0

So a belongs to $$(-\infty;-4/3)U(2;+\infty)$$

kamille · Answer

Ah, I made a mistake. It was x(a-1). But thanks for your help, anyway : ))

tamtoan · Answer

i would multiply both side by a-2 (provide a not equal to 2) ...to get

                 -2 < 3(a-2)
                 -2 < 3a - 6
                  4 <  3a
               4/3 < a              that would be your a :)

tamtoan · Answer

your answer have to exclude 2 because a cannot be 2 (denominator can't be zero)