Answer:
A.) no solution
Explanation:
You want to know the number of solutions of the equation 6x +1 = 2(3x -1).
Solution
We can expand the right side of the equation and subtract 6x:
6x +1 = 2(3x -1) . . . . . . given
6x +1 = 6x -2 . . . . . . . . eliminate parentheses
1 = -2 . . . . . . . . . . . . . . . subtract 6x from both sides
This is a false statement. No value of the variable x will make it true. The equation has no solution.
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Additional comment
The left and right sides of the equation define parallel lines. They have no point of intersection, so the equation has no solution.
If you actually mean 6z +1 = 2(3x -1), this resolves to z = x -1/2, which has infinitely many solutions (x, z).
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