To solve the linear equation:
[tex]\[
-12 + 3b - 1 = -5 - b
\][/tex]
we'll follow a step-by-step approach:
1. Combine like terms on each side of the equation:
- On the left side, combine [tex]\(-12\)[/tex] and [tex]\(-1\)[/tex]:
[tex]\[
-12 - 1 + 3b = -13 + 3b
\][/tex]
- On the right side, we have:
[tex]\[
-5 - b
\][/tex]
So the equation is now:
[tex]\[
-13 + 3b = -5 - b
\][/tex]
2. Move all terms involving [tex]\(b\)[/tex] to one side and constant terms to the other side:
- Add [tex]\(b\)[/tex] to both sides:
[tex]\[
-13 + 3b + b = -5
\][/tex]
- Simplify the terms:
[tex]\[
-13 + 4b = -5
\][/tex]
3. Isolate the term with [tex]\(b\)[/tex]:
- Add 13 to both sides to move the constants to the right side:
[tex]\[
-13 + 13 + 4b = -5 + 13
\][/tex]
Simplifying, this becomes:
[tex]\[
4b = 8
\][/tex]
4. Solve for [tex]\(b\)[/tex]:
- Divide both sides by 4 to isolate [tex]\(b\)[/tex]:
[tex]\[
b = \frac{8}{4}
\][/tex]
[tex]\[
b = 2
\][/tex]
Therefore, the solution to the equation [tex]\(-12 + 3b - 1 = -5 - b\)[/tex] is [tex]\(\boxed{2}\)[/tex].
