Question

while sandra is solving for y in terms of x, she sets up her problem and shows her work. in which step does her first error occur? assume the sides that look parallel are parallel.
step 1: \\( \frac { 2 } { 1 2 } = \frac { y } { x + 1 } \\)
step 2: \\( 1 2 y = 2 ( x + 1 ) \\)
step 3: \\( y = \frac { 2 ( x + 1 ) } { 1 2 } \\)
step 4: \\( y = \frac { x + 1 } { 6 } \\)

Explanation:

Step1: Analyze the proportion setup

The correct proportion should be based on the basic proportionality theorem (Thales' theorem). If \( CA\parallel ED\), then \(\frac{BA}{BD}=\frac{BC}{BE}\). Here, \(BA = 2\), \(BD=x + 1\), \(BC = y\), \(BE=3 + y\). The correct proportion is \(\frac{y}{3 + y}=\frac{2}{x + 1}\), not \(\frac{2}{y}=\frac{x + 1}{12}\) as in Step 1.

Answer:

Step 1