Question

if (bc = 7x), (cd = 6x - 10), and (bd = 10x + 14), 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 can set up the equation \(10x + 14=7x+(6x - 10)\).

Step2: Simplify the right - hand side of the equation

\(7x+(6x - 10)=7x + 6x-10=13x - 10\). So the equation becomes \(10x + 14=13x - 10\).

Step3: Solve for \(x\)

Subtract \(10x\) from both sides: \(14 = 13x-10x - 10\), which simplifies to \(14 = 3x-10\). Then add 10 to both sides: \(14 + 10=3x\), so \(24 = 3x\). Divide both sides by 3: \(x = 8\).

Step4: Find the value of \(BD\)

Substitute \(x = 8\) into the expression for \(BD\). \(BD=10x + 14\), so \(BD=10\times8+14=80 + 14=94\).

Answer:

94