Question

Given L || m || N, find the value of x:

\[9x - 6\]
m
\[6x + 6\]
A. \(x = -1\)
B. \(x = 2\)
C. \(x = 3\)
D. \(x = -2\)

Answer 1

Upon solving the equation set from the alternate interior angles (9x - 6 = 6x + 6), we find that x = 6, which does not match any of the answer choices provided. There may be a typo in the question or answer choices.

Step-by-step explanation:

The question involves solving for the variable x given two expressions that are set as equal because they correspond to alternate interior angles formed by two parallel lines L and N and a transversal m. Since the lines are parallel, we can assume that the alternate interior angles are equal. Therefore, we can set up an equation:

9x - 6 = 6x + 6

Now, we solve for x:

1. Subtract 6x from both sides of the equation:
2. 9x - 6 - 6x = 6 + 6
3. 3x - 6 = 12
4. Add 6 to both sides of the equation:
5. 3x = 18
6. Finally, divide both sides of the equation by 3 to find x:
7. x = 6

Therefore, the value of x is not listed among the answer choices given in the question (A. x = -1, B. x = 2, C. x = 3, D. x = -2). There may have been a typo in the problem or answer choices.