SOLUTION: Hi Free Tutors: I really appreciate the help you give on this site. I plugged an equation into the solver and it gave me the answer. However, I need step by step directions to b

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Hi Free Tutors: I really appreciate the help you give on this site. I plugged an equation into the solver and it gave me the answer. However, I need step by step directions to b      Log On


   

Question 9967: Hi Free Tutors:
I really appreciate the help you give on this site. I plugged an equation into the solver and it gave me the answer. However, I need step by step directions to be able to understand what I am doing. Here is my problem:
2/3(7/8-4x)-5/8<3/8 and this is the answer that the solver gave:x>5/32
Please show me the steps so that I can understand what I am doing?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2F3%29%2A%287%2F8-4x%29-%285%2F8%29+%3C+%283%2F8%29 i am assuming that it is 7/8 take away 4x rather than 8-4x all under 7?

If so, then first multiply every term by 3, to remove the "thirds" fraction. This leaves 2%2A%287%2F8-4x%29-3%285%2F8%29+%3C+3%283%2F8%29 which becomes %2814%2F8+-+8x%29+-%2815%2F8%29+%3C+%289%2F8%29. Simplifying the lefthand side gives:

-1%2F8+-+8x+%3C+9%2F8. Now add 1/8 to both sides to give
-8x+%3C+10%2F8 and simplify the fraction
-8x+%3C+5%2F4

Now for the one difference of inequalities over "equalities"... if we EVER multiply or divide by any -ve number, the inequality symbol swap around.


Now we are going to divide both sides by -8, to leave 1x ie "x"... so we have

x > (5/4)/-8

we cannot divide fractions. But what we can do is swap the second fraction (the 8/1) upside down and the multiply instead, as:

x > -(5/4)*(1/8)
x > -5/32

jon.