Solve Linear Equation: 3(b-1)-4(-b+3)=-28 Step by Step

To solve the given equation $3(b-1)-4(-b+3)=-28$, let's follow these steps:

• Step 1: Distribute the constants.
• Step 2: Simplify by combining like terms.
• Step 3: Isolate the variable $b$.

Now, let's work through each step:
Step 1: Apply the distributive property.
Starting with $3(b-1)-4(-b+3)$, distribute the constants:
$3 \cdot (b) + 3 \cdot (-1) - 4 \cdot (-b) - 4 \cdot 3 = 3b - 3 + 4b - 12$

Step 2: Combine like terms.
Combine the terms involving $b$ and the constant terms:
$3b + 4b - 3 - 12 = 7b - 15$
Set this equal to the right side of the equation:
$7b - 15 = -28$

Step 3: Solve for $b$.
Add 15 to both sides to isolate the term with $b$:
$7b = -28 + 15$

This simplifies to:
$7b = -13$

Finally, divide both sides by 7 to solve for $b$:
$b = \frac{-13}{7}$

Therefore, the solution to the problem is $b = -1\frac{6}{7}$.

Reviewing the answer choices, our solution $b = -1\frac{6}{7}$ matches the correct answer choice.