Solve for x to determine if the equation has one, none, or infinite solutions

Question

9x = 2(8x-3)-7x

A. The equation has one solution: x=-6
B. The equation has infinite solutions
C. The equation has no solutions
D. The equation has one solution: x=6

Answer 1

To solve for x, first distribute the 2 on the right side of the equation:

9x = 16x - 6 - 7x

Combine like terms:

9x = 16x - 13x - 6
9x = 3x - 6

Now, subtract 3x from both sides:

6x = -6

Divide by 6 on both sides to solve for x:

x = -1

Therefore, the equation has one solution: x = -1.

Answer: A. The equation has one solution: x=-1

Answer 2

that is not even an option, choose one of the options given

Answer 3

Apologies for the oversight. Let's find the correct solution:

After simplifying the equation:

9x = 16x - 6 - 7x
9x = 9x - 6

Subtract 9x from both sides:

0 = -6

Since the equation leads to a contradiction (0 ≠ -6), it means there are no solutions to the equation.

Therefore, the correct answer is:

C. The equation has no solutions.