Question

if de = x + 5, ef = 4, and df = 10x, what is de?
d---e---f (with de labeled x + 5, ef labeled 4, df labeled 10x)
simplify your answer and write it as a proper fraction, mixed number, or integer.
submit

Explanation:

Step1: Use segment addition postulate

From the number line, we know that \( DE + EF = DF \). Substituting the given expressions, we get \((x + 5)+4 = 10x\).

Step2: Simplify and solve for \( x \)

Simplify the left - hand side: \(x+5 + 4=x + 9\). So the equation becomes \(x + 9=10x\).
Subtract \(x\) from both sides: \(9 = 10x-x\), which simplifies to \(9 = 9x\).
Divide both sides by 9: \(x=\frac{9}{9}=1\).

Step3: Find the length of \( DE \)

We know that \( DE=x + 5\). Substitute \(x = 1\) into the expression for \( DE \): \(DE=1 + 5=6\).

Answer:

\(6\)