Question

What is true about the solution to the following linear equation?

-12 + 3b - 1 = -5 - b
a) One solution: b = 2
b) No solution
c) One solution: b = -2
d) Infinite solutions

Answer 1

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).