Question

Point C is on line segment \overline{BD} BD . Given CD=x,CD=x, BC=5x-5,BC=5x−5, and BD=2x+7,BD=2x+7, determine the numerical length of \overline{CD}. CD .

Answer 1

`CD = 3`

Explanation:

Given

`CD = x`

`BC = 5x - 5`

`BD = 2x + 7`

Required

Determine CD

Since, C is a point on BD, the relationship between the given parameters is;

`BD = BC + CD`

Substitute the values of BD, BC and CD

`2x + 7 = 5x - 5 + x`

Collect Like Terms

`2x - 5x - x = -5 - 7`

`-4x = -12`

Divide both sides by -4

`(-4x)/(-4) = (-12)/(-4)`

`x = 3`

To determine the length of CD;

Substitute 3 for x in
`CD = x`

Hence;

`CD = 3`