Chapter 1.5, Problem 25E

To determine

To explain:

The error and then correct equation for the following equation:

  

Answer to Problem 25E

The error of given solving equation is first need to collect $x$ terms on one side and remaining terms are on other side as need the solution of $x$ .

The solution is $x=3+\frac{1}{2}y$

Explanation of Solution

Given information:

  

From the image:

The main equation is $12-2x=-2\left(y-x\right)$ .

On solving:

  $\begin{array}{l}12-2x=-2\left(y-x\right)\\ -2x=-2\left(y-x\right)-12\\ x=\left(y-x\right)+6\end{array}$

Here, in the second step of the equation need to collect all $x$ terms on one side and remaining terms are on other side.

Now, need to solve the equation for $x$ by using correct method as:

  $\begin{array}{l}12-2x=-2\left(y-x\right)\\ 12-2x=-2y+2x\end{array}$

Now, add $2x$ on both sides of above equation:

  $\begin{array}{l}12-2x=-2y+2x\\ 12-2x+2x=-2y+2x+2x\\ 12=-2y+4x\end{array}$

Switch both sides:

  $-2y+4x=12$

Now, add $2y$ on both sides of above equation:

  $\begin{array}{l}-2y+4x=12\\ -2y+2y+4x=12+2y\\ 4x=12+2y\end{array}$

Divide by $4$ :

  $\begin{array}{l}4x=12+2y\\ \frac{4}{4}x=\frac{12+2y}{4}\\ x=3+\frac{1}{2}y\end{array}$