Question

if bc = 6, cd = x + 3, and bd = 3x - 11, what is bd? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $BD=BC + CD$, we substitute the given expressions: $3x-11=6+(x + 3)$.

Step2: Simplify the right - hand side

$3x-11=6+x + 3$, which simplifies to $3x-11=x + 9$.

Step3: Isolate the variable $x$

Subtract $x$ from both sides: $3x-x-11=x-x + 9$, resulting in $2x-11=9$.

Step4: Add 11 to both sides

$2x-11 + 11=9+11$, so $2x=20$.

Step5: Solve for $x$

Divide both sides by 2: $\frac{2x}{2}=\frac{20}{2}$, giving $x = 10$.

Step6: Find the value of $BD$

Substitute $x = 10$ into the expression for $BD$: $BD=3x-11=3\times10-11$.
$BD=30 - 11=19$.

Answer:

19