Question

solve for x. x = (simplify your answer. type an integer or a simplified fraction.)

Explanation:

Step1: Apply the Basic Proportionality Theorem (Thales' theorem) which states that if a line is drawn parallel to one side of a triangle, intersecting the other two sides, then it divides those sides proportionally. Here, we can set up the proportion $\frac{3}{7}=\frac{6}{x}$.

Step2: Cross - multiply to solve for $x$. Cross - multiplying gives us $3\times x = 7\times6$. So, $3x = 42$.

Step3: Divide both sides of the equation by 3 to isolate $x$. $\frac{3x}{3}=\frac{42}{3}$, which simplifies to $x = 14$.

Answer:

14