Question

point d is on line segment \\(\overline{ce}\\). given \\(de = x + 2\\), \\(cd = 3x + 2\\), and \\(ce = 5x + 2\\), determine the numerical length of \\(\overline{ce}\\).

Explanation:

Step1: Use segment addition postulate

Since D is on \(\overline{CE}\), we know that \(CD + DE = CE\). Substituting the given expressions: \((3x + 2)+(x + 2)=5x + 2\)

Step2: Simplify left side

Combine like terms: \(3x + x+2 + 2 = 5x + 2\) which simplifies to \(4x + 4 = 5x + 2\)

Step3: Solve for x

Subtract \(4x\) from both sides: \(4 = x + 2\). Then subtract 2 from both sides: \(x = 2\)

Step4: Find length of CE

Substitute \(x = 2\) into \(CE = 5x + 2\): \(CE = 5(2)+2 = 10 + 2 = 12\)

Answer:

12