To solve for \( x \), we can use the fact that angles formed by a transversal intersecting parallel lines have relationships that we can exploit. In this case, angle E and angle B can be considered alternate interior angles.
Given:
- Angle E = \( 3x + 18 \)
- Angle B = \( 14x - 8 \)
Since angles E and B are equal (because they are alternate interior angles), we can set up the equation:
\[ 3x + 18 = 14x - 8 \]
Now, we will solve for \( x \):
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Subtract \( 3x \) from both sides: \[ 18 = 14x - 3x - 8 \] \[ 18 = 11x - 8 \]
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Add 8 to both sides: \[ 18 + 8 = 11x \] \[ 26 = 11x \]
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Divide both sides by 11: \[ x = \frac{26}{11} \]
Thus, the value of \( x \) is \( \frac{26}{11} \).
The correct answer is:
\( \frac{26}{11} \)