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Sagot :
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].
[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].
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