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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

Respuesta :

MrRoyal

Answer:

[tex]BD = 19[/tex]

Step-by-step explanation:

Given

[tex]CD = 2x[/tex]

[tex]BD = 3x + 4[/tex]

[tex]BC = 2x -1[/tex]

Required

Find BD

Since C is on BD, we have:

[tex]BD = BC + CD[/tex]

Substitute values for BD, BC and Cd

[tex]3x + 4 = 2x - 1 + 2x[/tex]

Collect Like Terms

[tex]3x - 2x - 2x = -1 - 4[/tex]

[tex]-x = -5[/tex]

Multiply through by -1

[tex]x = 5[/tex]

Substitute 5 for x in [tex]BD = 3x + 4[/tex]

[tex]BD = 3 * 5 + 4[/tex]

[tex]BD = 19[/tex]