Question

1. 21 x - 3 27 x - 1

Explanation:

Step1: Set up proportion

Since the lines are parallel, we can set up the proportion $\frac{21}{x - 3}=\frac{27}{x - 1}$ based on the property of similar - shaped segments formed by parallel lines.

Step2: Cross - multiply

Cross - multiplying gives us $21(x - 1)=27(x - 3)$.
Expanding, we get $21x-21 = 27x-81$.

Step3: Solve for x

First, move the x - terms to one side and the constants to the other side:
$27x-21x=81 - 21$.
$6x=60$.
Dividing both sides by 6, we have $x = 10$.

Answer:

$x = 10$