Question

Point C is on line segment \overline{BD} BD . Given CD=2x,CD=2x, BD=3x+4,BD=3x+4, and BC=2x-1,BC=2x−1, determine the numerical length of \overline{BD}. BD

Answer 1

`BD = 19`

Explanation:

Given

`CD = 2x`

`BD = 3x + 4`

`BC = 2x -1`

Required

Find BD

Since C is on BD, we have:

`BD = BC + CD`

Substitute values for BD, BC and Cd

`3x + 4 = 2x - 1 + 2x`

Collect Like Terms

`3x - 2x - 2x = -1 - 4`

`-x = -5`

Multiply through by -1

`x = 5`

Substitute 5 for x in
`BD = 3x + 4`

`BD = 3 * 5 + 4`

`BD = 19`