Question 63346
2/3(7/8–4x)–5/8=3/8<br>

Plus (5/8) both sides
2/3(7/8-4x)=8/8  8/8=1, replace 8/8 with 1.
2/3(7/8-4x)=1  That simplifies things.  Divide by 2/3 on both sides
7/8-4x=1/(2/3)<br>

Let's look at {{{1/(2/3)}}}.  1 is the same thing as 1/1, so the fraction is {{{(1/1)/(2/3)}}}.  To divide a fraction by another, multiply the first fraction by the <b>reciprocal</b> of the other.  To obtain the reciprocal, simply switch the <I>numerator</i> (number on top) with the <i>denominator</i> (number on botton).  Applying this, the equation yields {{{(1/1)*(3/2)}}}.  To multiply, simply multiply the numerators to obtain the product numerator, and the denominators likewise.  {{{(1/1)*(3/2)=(1*3)/(1*2)=3/2}}}.  Getting back to the equation,<br>

7/8-4x=3/2  Minus 7/8 on both sides
-4x=(3/2)-(7/8)<br>

To subtract fractions, we need a common denominator.  We obtain this by finding a common factor, eight in this case.  Not to commit confusion, but the factor can be a lot of numbers.  It could be 16, 32, even 5 if we complicated the equation (6.5/5-(35/8)/5), but ideally we find the <i>least common denominator</i> which will allow us integers' comfort.  Depending on your level of math, you may want to ignore this paragraph.  Anyways, the common denominator is 8.
<br>
-4x=12/8-7/8  I multiplied both the numerator and denominator of the 3/2 by 4 to get the common denominator of 8.  Simplify.<br>

-4x=5/8  Now divide by -4.
x=(5/8)/-4  -4 is the same as (-4/1) so replace -4 with its equivalent for proof's sake:
x=(5/8)/(-4/1)  Multiply first fraction with reciprocal of the other.
x=(5/8)*(1/-4)=-5/40  simplify the fraction:
-1/8, or -.125<br>

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