Final answer:
To write an equation with the solution b = -6, we could multiply both sides of the solution by a number and adjust with fractions. However, a correct option from the choices provided can be found by algebraically solving for b in each and finding the one that results in b = -6.
Step-by-step explanation:
The equation we are looking to write must have the solution b = -6. We can start by multiplying both sides of this solution by a number and then adding or subtracting a fraction to create an equation that has the same solution. Let's explore one example:
- Take 2b = -12 (multiplying both sides by 2).
- Next, add 1/2 to both sides to get 2b + 1/2 = -11 1/2.
- Since -11 1/2 is equivalent to -23/2, our equation is 2b + 1/2 = -23/2.
This is not one of the options given to us, but using the same logic, we can check the given options to determine which one would have b = -6 as a solution. We use algebraic methods to solve for b in each option and check which one equates to -6.