Solve 1/3(x-3)<x-2/4 it is an inequality.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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}

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jellybean1977's profile pic

jellybean1977 | High School Teacher | (Level 1) Adjunct Educator

Posted on

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.