Question

I don't understand how to do this problem.

Answer 1

Answers: 

x = 4
EF = 14
CF = 7
EC = 7

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Work Shown:

C is the midpoint of segment EF. This means that EC = CF. In other words, the two pieces are congruent. 

Use substitution and solve for x
EC = CF
5x-13 = 3x-5
5x-13+13 = 3x-5+13
5x = 3x+8
5x-3x = 3x+8-3x
2x = 8
2x/2 = 8/2
x = 4

Now that we know that x = 4, we can use this to find EC and CF

Let's compute EC
EC = 5x - 13
EC = 5*x - 13
EC = 5*4 - 13 ... replace x with 4
EC = 20 - 13
EC = 7

Let's compute CF
CF = 3x - 5
CF = 3*x - 5
CF = 3*4 - 5 ... replace x with 4
CF = 12 - 5
CF = 7

As expected, EC = CF (both are 7 units long).

By the segment addition postulate, we can say EC+CF = EF

EC+CF = EF
EF = EC+CF
EF = 7+7
EF = 14