1. Solve: 2 5 1 - - - = -
3 6 x
Solution: The LCM of all denominators is
6x. Multiply each side of the
equation by 6x.
6x((2/3) - (5/6)) = 6x(1/x)
Use the distributive law of multi-
plication, which says a(b + c) =
ab + ac, to rewrite the
6x(2/3) - 6x(5/6) = 6x(1/x)
Multiply each group of terms
(12x/3) - 30x/6 = 6x/x
Perform each of the indicated
4x - 5x = 6
Solve for x.
Combine like terms.
-x = 6
Multiply each side by -1.
x = -6
Why would you Mutliply by 6X rather than just 6?
If you multiply by only 6, you will still have a fraction, with an x in the denominator. Now, the problem was to solve for x. You want to manipulate this equation so that you end with x = some number. It's a little more difficult to solve for x if it's in the denominator, isn't it?
other problems like this will require the same technique or a more complex variation.
You should stay with it until you've got it...
You want to find the value of x, but it's in the denominator position.
Both sides are equal, so if we multiply both sides by the same value,
they will still be equal.
Therefore multiply both sides by x
since then we have an x no longer in the denominator position.
Also multiply both sides by 6 to get rid of all fractions.
Makes things much clearer as far as x is concerned.