Answer
$cx-a+b=2b$
$x=\frac{a+b}{c}$
$b+a=cx$
Work Step by Step
We will take each equation and bring $cx$ and $a$ on the left side and $b$ on the right side.
$\textbf{Case 1}$: $cx-a+b=2b$
Subtract $b$ from each side $$cx-a=b.$$ This equation is equivalent to the given equation.
$\textbf{Case 2}$: $0=cx-a+b$
Subtract $b$ from each side $$-b=cx-a$$ which can be written $$cx-a=-b.$$ This equation is not equivalent to the given equation.
$\textbf{Case 3}$: $2cx-2a=\frac{b}{2}$
Divide each side by $2$ $$cx-a=\frac{b}{4}.$$ This equation is equivalent to the given equation.
$\textbf{Case 4}$: $x-a=\frac{b}{c}$
Multiply each side by $c$ $$cx-ca=b.$$ This equation is not equivalent to the given equation.
$\textbf{Case 5}$: $x=\frac{a+b}{c}$
Multiply each side by $c$ $$cx=a+b.$$ Subtract $a$ from each side $$cx-a=b.$$ This equation is equivalent to the given equation.
$\textbf{Case 6}$: $b+a=cx$
Subtract $a$ from each side $$b=cx-a$$ which can be written $$cx-a=b.$$This equation is equivalent to the given equation.
