SOLUTION: So I have been doing some workbooks to refresh myself in algebra lately to get back into school and a ran into a problem that for the life of me I cannot understand, its a Linear E

Question 551481: So I have been doing some workbooks to refresh myself in algebra lately to get back into school and a ran into a problem that for the life of me I cannot understand, its a Linear Equation that in order to find the value of X you have to eliminate the fractions to break it down, now the question in the book reads:
"Solve The Following Equation: 5 - (1/6)x = {-(2/3)}x "
now i have worked it down several times but it never matched what the answer in the workbook of " 30-x=9x "
from what the book says it should be its easy to find the solution is " X=3 " but when I work down the original equation I get this:
5 - (1/6)x = {-(2/3)}x ***convert to fractions**
5/1 - x/6 = -(3x/2) **next multiplied each term by the LCD of 6,or 6/1**
5/1*6/1 - x/6*6/1 = {-(3x/2)}*6/1 ***ok......
here is where i am confused, after canceling out the denominators my ending equation is " 30-x= -9x " now it has been along time since i have done any math assignments but i thought a negative multiplied by a positive stayed a negative # but my book says it becomes positive? is that right? Is -3x*6= to 9x? if so why? i thought like-signs always made a positive in multiplication

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
not wishing to demean your book, but...substituting the "solution" into the original equation

5 - (1/6)(3) = {-(2/3)}(3) ___ 5 - (1/2) = -(6/3)...I don't think so...

"Solve The Following Equation: 5 - (1/6)x = {-(2/3)}x "

multiplying by 6 to clear fractions ___ 30 - x = -4x ___ x = -10

something is amiss, but what?

the only "glitch" I could see is ___ how did {-(2/3)}x become (-3x/2) between your 1st and 2nd step?
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