in parallelogram ABCD, diagonals AC and DB inersect at E, AE=3x-4, and EC=x+12. What is the value of x

Question

I need help

Answer 1

Since ABCD is a parallelogram, opposite sides are parallel and equal.  The diagonals of a parallelogram bisect each other at E.

 

therefore 

AE = EC

 

3x - 4 = x + 12

 

we want to get all our variables on one side the equal sign (lets say the left side), and all the constants on the other side (the right side) of the equal sign.

 

so:

subtract x from both sides

 

3x - x - 4 = x - x +12

 

2x - 4 = 12

 

now add four to both sides to get all the constants on the right side.

 

2x - 4 +4 = 12 + 4

 

2x = 16

 

divide both sides by 2 to isolate the variable x

 

2x ÷ 2 = 16 ÷ 2

 

x = 8

 

CHECK BACK YOUR ANSWER by substituting 8 into your original equation to see if the left side of the equation equals the right side of your equation.

 

3x - 4 = x + 12

3(8) - 4 = 8 + 12

24 - 4 = 8 + 12

20 = 20

 

8 is the correct answer

Answer 2

The diagonals of a parallelogram bisect each other.

 

So AE = EC

 

3x - 4 = x + 12

 

etc.