Question

find the length indicated. 15) find ce b 3x + 47 c d 10 e 27 + x x + 26 cd = bd - be

Explanation:

Step1: Set up equation based on segment - addition

Since \(BD=BC + CD\) and \(BD = 27 + x\), \(BC=3x + 47\), \(CD=x + 26\), we have \(27+x=(3x + 47)+(x + 26)\).

Step2: Simplify the right - hand side of the equation

\(27+x=3x + 47+x + 26\), which simplifies to \(27+x=4x+73\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(27=4x - x+73\), so \(27 = 3x+73\). Then subtract 73 from both sides: \(3x=27 - 73=-46\), and \(x=-\frac{46}{3}\).

Step4: Find \(CE\)

Since \(CE=CD + DE\) and \(CD=x + 26\), \(DE = 10\), then \(CE=(x + 26)+10=x + 36\).
Substitute \(x =-\frac{46}{3}\) into the expression for \(CE\): \(CE=-\frac{46}{3}+36=\frac{-46 + 108}{3}=\frac{62}{3}\).

Answer:

\(\frac{62}{3}\)