Question

if $bc = 2x$, $cd = 6x - 11$, and $bd = 6x + 17$, what is $bd$?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the diagram, \( BD = BC + CD \). Substitute the given expressions: \( 6x + 17 = 2x + (6x - 11) \)

Step2: Simplify the equation

Simplify the right - hand side: \( 6x + 17 = 2x+6x - 11\), which becomes \( 6x + 17 = 8x - 11\)

Step3: Solve for x

Subtract \( 6x \) from both sides: \( 17=2x - 11\). Then add 11 to both sides: \( 2x=17 + 11=28\). Divide both sides by 2: \( x = 14\)

Step4: Find the length of BD

Substitute \( x = 14\) into the expression for \( BD \): \( BD=6x + 17=6\times14+17=84 + 17 = 101\)

Answer:

\(101\)