Solving for b for equation $3a−5=−4b+1$ I have a math problem, and I'm trying to solve for 'b'. The problem answer shows that the first step is going from Step 1 to Step 2. I don't understand how they are doing this. How does the $-4b$ magically become positive and then 5 become 6? I'm obviously missing something. What is it?
\begin{align*}
    3a−5&=−4b+1\\ 
    4b &= 6 -3a\end{align*}
 A: What we are really invoking are some nice (intuitive properties) of the numbers. For starters note that $b$ does not become positive. Instead we add $4b$ on both sides of the equation:
$$3a-5=-4b+1\implies 3a-5+4b=-4b+1+4b$$.
Hence we $3a-5+4b=1$. Now add $5-3a$ on both sides to get $4b=6-3a$.
A: $$3a-5 = -4b+1 \to 3a -5 +4b = -4b + 4b +1$$
adding $4b$ to both sides
$$3a-5+4b=1 \to 3a -5 +5 +4b =1+5$$ 
adding 5 to both sides
$$3a +4b =6 \to 3a +4b -3a = 6 - 3a$$ 
taking 3a from both sides
 $$4b = 6-3a$$
A: HINT: Remember that at each step, what we do to one side of the equation we must do to the other. 
Try to find a series of steps that would lead you to that answer. 

 $3a−5=−4b+1 \implies 3a=-4b+6 \implies 4b+3a = 6 \implies 4b = 6 -3a$

A: The basic principle is: If $x\color{red}{+c}=y$, then $x=y\color{blue}{-c}$.
So, the missing steps are:
$$\begin{align}
3a\color{red}{−5} =−4b+1 & \implies 3a = - 4b + 1 \color{blue}{+ 5}
\\ \color{red}{3a}  = -4b + 6 & \implies  0 = {-4b} + 6 \color{blue}{- 3a}
\\  0 = \color{red}{-4b} + 6 - 3a & \implies \color{blue}{+4b } = 6 - 3a
\end{align}$$
