# How do I solve this proportion: 50 over 2t + 4  =  2t + 4 over 2 It's ok to use cross multiplication. 50/ (2t+4) = (2t+4) / 2

First we will cross multiply.

==> (2t+4)*(2t+4) = 2*50

==> (2t+4)^2 = 100.

Now we will take the root of both sides.

==> (2t+4) = +-10.

Then, we have two cases.

Let us solve each case.

==> (2t+4)= 10  ==> 2t = 6 ==>...

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50/ (2t+4) = (2t+4) / 2

First we will cross multiply.

==> (2t+4)*(2t+4) = 2*50

==> (2t+4)^2 = 100.

Now we will take the root of both sides.

==> (2t+4) = +-10.

Then, we have two cases.

Let us solve each case.

==> (2t+4)= 10  ==> 2t = 6 ==> t1= 3

==> (2t+4) = -10 ==> 2t = -14 ==> t2= -7.

Then there are two values for t.

t= { -7, 3}.

To check the answer, we will substitute with t1 and t2.

If t= -7 ==> 50/(2*-7 + 4) = (2*-7+4)/ 2

==> 50/ (-10) = -10/2

==> -5 = -5

If t= 3 ==> 50/(2*3+4) = (2*3+4)/2

==> 50/ (10) = (10)/ 2

==> 5 = 5.

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