Question

c is between d and b. cb = x + 11, db = 18, and dc = 2x + 7. draw and label the segment. x= cb=

Explanation:

Step1: Apply segment - addition postulate

Since \(C\) is between \(D\) and \(B\), we have \(DC + CB=DB\). So, \((2x + 7)+(x + 11)=18\).

Step2: Combine like - terms

\(2x+x+7 + 11=18\), which simplifies to \(3x+18 = 18\).

Step3: Isolate the variable term

Subtract 18 from both sides: \(3x+18−18=18 - 18\), resulting in \(3x=0\).

Step4: Solve for \(x\)

Divide both sides by 3: \(\frac{3x}{3}=\frac{0}{3}\), so \(x = 0\).

Step5: Find the length of \(CB\)

Substitute \(x = 0\) into the expression for \(CB\). \(CB=x + 11\), so \(CB=0 + 11=11\).

Answer:

\(x = 0\)
\(CB=11\)