Question

find the value of x so that b || c. (3x + 8)° (7x)° x = need help?

Explanation:

Step1: Identify Alternate Interior Angles

For lines \( b \parallel c \) cut by a transversal, alternate interior angles are equal. So, \( 3x + 8 = 7x \).

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:
\( 8 = 7x - 3x \)
Simplify: \( 8 = 4x \)
Divide by 4: \( x = \frac{8}{4} = 2 \). Wait, no—wait, maybe I mixed up. Wait, no, let's check again. Wait, maybe they are same - side? No, the angles: if \( b \parallel c \), the two angles \( (3x + 8)^\circ \) and \( (7x)^\circ \) should be equal (alternate interior). Wait, solving \( 3x + 8 = 7x \):
\( 8 = 7x - 3x \)
\( 8 = 4x \)
\( x = 2 \)? Wait, no, that seems too small. Wait, maybe I got the angle relationship wrong. Wait, maybe they are supplementary? Wait, no, the diagram: let's re - examine. The angle \( (3x + 8)^\circ \) and \( (7x)^\circ \): if \( b \parallel c \), maybe they are alternate interior angles, so equal. Wait, but let's do the algebra again.
\( 3x+8 = 7x \)
Subtract \( 3x \): \( 8 = 4x \)
\( x = 2 \). Wait, but let's check: if \( x = 2 \), \( 3x + 8=6 + 8 = 14 \), \( 7x = 14 \). Oh, right, so they are equal. So that works.

Answer:

\( x = 2 \)