Question

question point c is on line segment bd. given cd = 2x, bd = 3x + 4, and bc = 2x - 1, determine the numerical length of bd. answer attempt 1 out of 2 bd =

Explanation:

Step1: Use segment - addition postulate

Since \(BD=BC + CD\), we substitute the given expressions: \(3x + 4=(2x - 1)+2x\).

Step2: Simplify the right - hand side

\((2x - 1)+2x=2x+2x - 1=4x - 1\). So the equation becomes \(3x + 4=4x - 1\).

Step3: Solve for \(x\)

Subtract \(3x\) from both sides: \(3x+4-3x=4x - 1-3x\), which gives \(4=x - 1\). Then add 1 to both sides: \(4 + 1=x-1 + 1\), so \(x = 5\).

Step4: Find the length of \(BD\)

Substitute \(x = 5\) into the expression for \(BD\). Since \(BD=3x + 4\), then \(BD=3\times5+4=15 + 4=19\).

Answer:

19