Question

find x and select your answer on the next screen

Explanation:

Step1: Recall Angle Bisector Theorem (Perpendiculars)

Since \( AB \) is the angle bisector of \( \angle DAC \) (or the relevant angle), and \( BD \perp AD \), \( BC \perp AC \), by the Angle Bisector Theorem, the lengths of the perpendiculars from a point on the angle bisector to the two sides of the angle are equal. So \( BD = BC \).
Given \( BD = x + 7 \) and \( BC = 3x + 3 \), we set up the equation: \( x + 7 = 3x + 3 \).

Step2: Solve the Linear Equation

Subtract \( x \) from both sides: \( 7 = 2x + 3 \).
Subtract 3 from both sides: \( 4 = 2x \).
Divide both sides by 2: \( x = \frac{4}{2} = 2 \).

Answer:

\( x = 2 \)