Chapter 1.5, Problem 26E

To determine

To explain:

The error and then correct equation for the following equation:

  

Answer to Problem 26E

The error of given solving equation is first need switch sides. Then there is no $x$ term is available in $\left(3b\right)$ , so no need to take $x$ common from $\left(3b\right)$ .

The solution is $x=\frac{10+3b}{a}$

Explanation of Solution

Given information:

  

From the image:

The main equation is $10=ax-3b$ .

On solving:

  $\begin{array}{l}10=ax-3b\\ 10=x\left(a-3b\right)\\ \frac{10}{\left(a-3b\right)}=x\end{array}$

Here, in the second step of the equation need to switch sides to get solution of $x$ . Then another error is there is no $x$ term is available in $\left(3b\right)$ , so no need to take $x$ common from $\left(3b\right)$ as done in step (2): $10=x\left(a-3b\right)$ .

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

  $10=ax-3b$

Switch both sides:

  $ax-3b=10$

Now, add $3b$ on both sides of above equation:

  $\begin{array}{l}ax-3b=10\\ ax-3b+3b=10+3b\\ ax=10+3b\end{array}$

Divide by $a$ :

  $\begin{array}{l}ax=10+3b\\ \frac{a}{a}x=\frac{10+3b}{a}\\ x=\frac{10+3b}{a}\end{array}$