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

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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.

cross multiply:

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

square it:

(2t+4)^2 = 100.

take the root of both sides:

(2t+4) = +-10.

Set up an equation:

2t+4= 10

solve:

2t+4= 10

2t = 6

t= 3

2t+4 = -10

2t = -14

t= -7

t= -7 and 3

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

cross multiply:

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

since the parentheses are the same numbers we square it:

(2t+4)^2 = 100.

take the root of both sides:

(2t+4) = +-10.

Set up the equation:

2t+4= 10

and

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

solve:

2t+4= 10

2t = 6

**t= 3**

2t+4 = -10

2t = -14

**t= -7**

**t= -7 and 3**

First we write the equation in the form given below:

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

We factor out both numerator and denominators on both sides:

2*25/2(t+2) = 2(t+2)/2.

25/(t+2) = (t+2). Reduced by2 through out.

We multiply both sides by t+2.

25 = (t+2)^2.

(t+2)^2= 25.

We take square root.

t+2 = - 5 Or t+2 = -5.

t = 5-2 = 3. Or t= -5-2 =-7.

Therefore t = 3, or t = -7.