Question

How many solutions does the equation 6z + 1 = 2(3x - 1) have?

A.) no solution
B.) one solution
C.) infinitely many solutions

Answer 1

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.

__

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).

<95141404393>