Final answer:
The solution to the linear equation -12 + 3b - 1 = -5 - b is one value for b, which is b = 2. This is achieved by rearranging and isolating the variable b, giving the answer as (a) One solution: b = 2.
Step-by-step explanation:
To solve the equation -12 + 3b - 1 = -5 - b, we need to rearrange and combine like terms to isolate the variable b. First, combine the constants on the left side:
-12 - 1 + 3b = -5 - b
Which simplifies to:
-13 + 3b = -5 - b
Next, we need to get all the b terms on one side. Add b to both sides of the equation:
-13 + 3b + b = -5 - b + b
This simplifies to:
-13 + 4b = -5
Now, add 13 to both sides to get:
4b = 8
Finally, divide both sides by 4 to solve for b:
b = 2
Therefore, the solution to the equation is one value for b, which is b = 2, corresponding to option (a).