SOLUTION: Solve for x ((x + 1) /3)

SOLUTION: Solve for x ((x + 1) /3) - ((x-1) / 5) = (x/4)

Question 369504: Solve for x
((x + 1) /3) - ((x-1) / 5) = (x/4)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Before I start, I am going to change the subtraction on the left side into the addition of the opposite because subtracting fractions is an extremely common source of errors.

As usual there are several ways to solve an equation like this. The way I like starts by eliminating the fractions. This can be done by finding the Lowest Common Denominator (LCD) of all the denominators on both sides and then multiplying both sides by this LCD.

Your denominators are 3, 4 and 5. the LCD of these is simply their product: 3*4*5. So we will multiply both sides by 3*4*5:

On the left side of the equation we need to use the Distributive Property to multiply it correctly:

Now the denominators of each fraction cancel out!

leaving:
4*5*(x + 1) + 3*4*(-x+1) = 3*5*x
which simplifies as follows:
20x + 20 + (-12x) + 12 = 15x
8x +32 = 15x
This is a fairly simple equation to solve. First we want the x term's on just one side. So I'll subtract 8x from each side:
32 = 7x
And then divide both sides by 7:

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