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1/2y+20= 3y

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As in all algebraic equations you must do the same thing on both sides of the equation.   The goal is to isolate the variable on one side and the constant on the other side of the equation.

First subtract 1/2y from both sides

1/2y +20 = 3y

-1/2y           -1/2y

________________

20= 3y-1/2y

20=2 1/2y

Since we have a mixed fraction, convert it to an improper fraction by multiplying the denominator (2) by the whole number (2) and then adding the numerator (1)  (2*2) + 1 = 5.  5  is the numerator for our improper fraction; the denominator is still 2.  So our improper fraction is 5/2.

Now our equation is

20 = 5/2y

To isolate y, we must divide both sides by 5/2

20/ (5/2) = y

which is the same as (20/1) / (5/2) = y

When we divide fractions, we flip one of the fractions and multiply, so now our eqation is

20/1 X 2/5 = y

40/5 = y

8 = y

To prove this, we substitute 8 for y in the original equation:

(1/2) 8 + 20 = 3(8)

4 + 20 = 24

24 = 24

In a triangle and the mid segment is 1/2 of the base.  Since the mid-segment is 8, the base of the triangle is 16.