Question

if de = x - 5, ef = 18, and df = 3x - 19, what is df?
diagram: line segment with endpoints d, f; point e between d and f. de labeled ( x - 5 ), ef labeled 18, df labeled ( 3x - 19 )
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment addition postulate

From the diagram, \( DF = DE + EF \). Substitute the given expressions: \( 3x - 19=(x - 5)+18 \)

Step2: Solve for \( x \)

Simplify the right side: \( 3x - 19=x + 13 \)
Subtract \( x \) from both sides: \( 2x - 19 = 13 \)
Add 19 to both sides: \( 2x=32 \)
Divide by 2: \( x = 16 \)

Step3: Find \( DF \)

Substitute \( x = 16 \) into \( DF = 3x - 19 \): \( DF=3(16)-19 \)
Calculate: \( DF = 48 - 19=29 \)

Answer:

29