SOLUTION: (2x – 5)/3 – 3/2 = (x + 4)/5 Solve for x

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Question 70487: (2x – 5)/3 – 3/2 = (x + 4)/5
Solve for x
Found 2 solutions by pleasuretohelp, bucky:
Answer by pleasuretohelp(9) About Me  (Show Source):
You can put this solution on YOUR website!
(2x – 5)/3 – 3/2 = (x + 4)/5
First, we group the ones that have an x together.
Move (x + 4)/5 to the left, so we have:
(2x – 5)/3 – 3/2 - (x + 4)/5 = 0
Second, since - 3/2 does not have an x, we move it to the right.
(2x – 5)/3 – (x + 4)/5 = 3/2
Third, find the common denominator.
The common denominator for 3, 2, and 5 is 30.
(10 * (2x – 5)/(3 * 10)) – (6 * (x + 4)/(5 * 6)) = (15 * 3/(2 * 15))
Fourth, simplify the whole equation.
(20x - 50)/30 - (6x + 24)/30 = 45/30
Fifth, since all of them have the same common denominator, we can eliminate it from the equation.
(20x - 50) - (6x + 24) = 45
Sixth, we can simplify the equation.
20x - 50 - 6x - 24 = 45
14x - 74 = 45
Sixth, move - 74 to the right.
14x = 45 + 74
14x = 119
Seventh, divide both sides by 14.
14x/14 = 119/14
x = 8 1/2

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
%282x-5%29%2F3+-+%283%2F2%29+=+%28x+%2B+4%29%2F5
.
You cannot add or subtract fractions unless they have a common denominator. In this problem
we can use a common denominator of 30 because all the denominators in the problem are factors
of 30. There are 3 terms in this problem and we need to get each term so it has a denominator
of 30.
.
The first term is %28%282x-5%29%2F3%29. We could multiply this fraction by 10%2F10
and it would not change the value of the fraction because 10%2F10 equals 1, so we are
multiplying the original fraction by 1. When we multiply the fraction by 10%2F10, the
result is 10%2A%282x-5%29%2F30 and this simplifies to %2820x-50%29%2F30.
.
The second term is 3%2F2 and to get the denominator to equal 30, we multiply the fraction
by 15%2F15. The result of this multiplication is that the denominator becomes 30,
and the numerator becomes 15%2A3+=+45. So the term is now converted to 45%2F30
.
The last term is %28x%2B4%29%2F5. To give this a denominator of 30 we multiply the fraction
by 6%2F6. The denominator becomes 30 and the numerator becomes 6%2A%28x%2B4%29
which simplifies to 6x+%2B+24. So the fraction is converted to %286x%2B24%29%2F30.
.
Substituting these three results into the original equation converts the problem to:
.
%28%2820x-50%29%2F30%29-%2845%2F30%29+=+%28%286x%2B24%29%2F30%29
.
Since the denominator 30 is common to all terms we can eliminate it by multiplying
all the terms in the equation by 30. The result is that the multiplier of 30 cancels with
the denominator of 30 in all terms and the problem now involves dealing with only the
numerators as follows:
.
20x-50-45+=+6x%2B24
.
Combine the -50 and the - 45 on the left side to get:
.
20x-95+=+6x%2B24
.
Add 95 to both sides to cancel the -95 on the left side. This results in:
.
20x+=+6x%2B119
.
Subtract 6x from both sides to eliminate it on the right side.
.
14x+=+119
.
And finally, divide both sides by 14 to get:
.
x+=+119%2F14+=+8.5
.
That's the answer to the problem. Hope this helps you to see a way of solving fractional
problems such as these.