Question

Which of the following equations have exactly one solution?

1) [6x-6=6x 15]
2) [6x-15=6x 15]
3) [6x 15=6x 15]
4) [6x-6=15x 15]

Answer 1

Among the given options, the equation that has exactly one solution is 6x-6=15x+15. After rearranging and solving for x, this equation results in a single value for x, indicating exactly one solution.

Step-by-step explanation:

When determining which equations have exactly one solution, we are looking for an equation where, after simplifying and attempting to solve for the variable, we end up with a statement where the variable has a single value. In the given options, the equation that has exactly one solution is: 6x-15=6x+15.

1. To solve for x, we subtract 6x from both sides: -15 = 15, which is not possible. This equation has no solution, as we cannot find any value of x that makes the equation true.
2. The equation 6x+15=6x+15 is true for all values of x, making it an identity with infinitely many solutions.
3. For the equation 6x-6=15x+15, we solve for x by subtracting 6x from both sides and then subtracting 15 from both sides to isolate x, which will give us the one solution we are looking for.

Therefore, the correct equation is the fourth one: 6x-6=15x+15.