Final answer:
Option B) 4y - 6 = 2y + 9, is the equation that, by adding a single negative sign in front of the 9, will be transformed from having no solutions to an equation with infinite solutions, as it will result in 4y - 6 = 2y - 9, or 2y = 2y. option B
Step-by-step explanation:
To create an equation with no solutions that can be transformed into an equation with infinite solutions by inserting a single negative sign, we should look for an equation where both sides can become identical by the addition of a negative sign.
The correct choice would be option B) 4y - 6 = 2y + 9. This equation has no solutions as it stands because if you solve for y, you get a false statement.
Here is the process of transforming the equation with no solutions to one with infinite solutions:
Original equation: 4y - 6 = 2y + 9
Subtract 2y from both sides: 2y - 6 = 9
Now, insert a negative sign in front of 9, changing it to -9: 2y - 6 = -9
Add 6 to both sides: 2y = -3
Divide by 2: y = -3/2
Finally, replace the original 9 with -9 in the equation to make the transformation:
Transformed equation: 4y - 6 = 2y - 9
By inserting a negative sign before the 9, we have created a scenario where upon simplifying both sides of the equation, we end up with 2y = 2y, which is true for all values of y, giving us infinite solutions. Option B