If BC is 4x and CD is 2x+3, find x, BC, CD, and BD

Question

C is the midpoint of segment BD. If BC is 4x and CD is 2x+3, find x, BC, CD, and BD.

Answer 1

If you visualize this line segment BCD, we can see that half of the line (B to C) is 4x, and the other half (C to D) is equal to 2x+3. We know that C is the midpoint, so that means that the two sides are equal. So we can set this up using the equation 4x = 2x+3

 

To solve this equation, we must get the x by itself on one side of the equal sign. 

 

4x = 2x + 3

-2x   -2x 

2x = 3

/2      /2

x = 3/2 or 1.5

 

To find BC, CD, and BD, you simply plug in the x for both lengths. 4 multiplied by x, which we know is 1.5, is equal to 6. So BC is 6, and since this is equal to CD, we know that CD is also 6. And for BD we just add together both sides. So BD is 12.