Let's solve the linear equation step by step:
Given:
[tex]\[
-12 + 3b - 1 = -5 - b
\][/tex]
1. Simplify both sides of the equation.
On the left-hand side:
[tex]\[
-12 + 3b - 1 = -13 + 3b
\][/tex]
So the equation becomes:
[tex]\[
-13 + 3b = -5 - b
\][/tex]
2. Next, let's collect all the terms involving \( b \) on one side and the constant terms on the other side.
Add \( b \) to both sides:
[tex]\[
-13 + 3b + b = -5 - b + b
\][/tex]
[tex]\[
-13 + 4b = -5
\][/tex]
3. Isolate the term containing \( b \) by adding 13 to both sides:
[tex]\[
-13 + 4b + 13 = -5 + 13
\][/tex]
[tex]\[
4b = 8
\][/tex]
4. Now, solve for \( b \) by dividing both sides by 4:
[tex]\[
b = \frac{8}{4}
\][/tex]
[tex]\[
b = 2
\][/tex]
Therefore, the solution to the equation is
[tex]\[
b = 2
\][/tex]
