Question

solve the linear equation for b. if no solution exists, enter no solution. if the equation has infinite solutions, enter all real numbers. -(-b + 2) - 48 = -3(-5b + 12) show your work here

Explanation:

Step1: Simplify both sides

First, simplify the left - hand side: $-(-b + 2)-48=b - 2-48=b-50$.
Then, simplify the right - hand side: $-3(-5b + 12)=15b-36$.
So the equation becomes $b - 50=15b-36$.

Step2: Move terms with b to one side

Subtract $b$ from both sides: $b - b-50=15b - b-36$, which simplifies to $-50 = 14b-36$.

Step3: Solve for b

Add 36 to both sides: $-50 + 36=14b-36 + 36$, so $-14 = 14b$.
Divide both sides by 14: $\frac{-14}{14}=\frac{14b}{14}$, which gives $b=-1$.

Answer:

$b = - 1$