We have to solve the inequality (1/3)*(x-3) < (x-2)/4
(1/3)*(x-3) < (x-2)/4
=> 4(x - 3) < 3(x - 2)
=> 4x - 12 < 3x - 6
=> 4x - 3x < 12 - 6
=> x < 6
The solution of the inequality is [-inf., 6}
First you need to distribute (multiply 1/3 by x and -3). This will give you
1/3x-1<(x-2)/4 I'm assuming that x-2 is all over 4 on the right side.
Then you'll have to multply both sides by 4 to get the x-2 alone on the right side. This will give you:
4/3x-4<x-2 Now you need to get the x's together. Do this by subtracting x from each side. This leaves you with:
1/3x-4<-2 Now it's much more simple, just add 4 to each side:
1/3x<2 Last, divide by 1/3 or multply by 3 on each side and get:
Hopefully that helps.