Question

if de = 2x - 9, ef = x + 1, and df = 19, what is ef? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set up the equation

Since \( DE + EF = DF \), substitute the given expressions: \( (2x - 9)+(x + 1)=19 \).

Step2: Simplify the left side

Combine like terms: \( 2x - 9 + x + 1 = 3x - 8 \). So the equation becomes \( 3x - 8 = 19 \).

Step3: Solve for x

Add 8 to both sides: \( 3x = 19 + 8 = 27 \). Then divide by 3: \( x=\frac{27}{3}=9 \).

Step4: Find EF

Substitute \( x = 9 \) into \( EF = x + 1 \): \( EF = 9 + 1 = 10 \).

Answer:

10