Question

Write a verbal description for each step of the equation solving process used to solve the following equations for x. Number 10

Answer 1

Given the equation:

`r\cdot\sqrt[]{(mx)/(n)+s}=t`

You can solve for "x" as follows:

1. You need to divide both sides of the equation by "r", in order to move that variable to the other side of the equation, without changing the balance:

`\begin{gathered} \frac{r\cdot\sqrt[]{(mx)/(n)+s}}{r}=(t)/(r) \\ \\ \sqrt[]{(mx)/(n)+s}=(t)/(r) \end{gathered}`

Notice that "r" is multiplying on the left side, then you need to use an inverse operation of the Multiplication in order to move it to the other side.

2. Now you have to square both sides of the equation in order to eliminate the square root on the left side, because they are inverse:

`\begin{gathered} (\sqrt[]{(mx)/(n)+s})^2=((t)/(r))^2 \\ \\ (mx)/(n)+s=(t^2)/(r^2) \end{gathered}`

3. The next step is to subtract "s" from both sides of the equation. Remember the Addition and Subtraction are inverse operations:

`\begin{gathered} (mx)/(n)+s-(s)=(t^2)/(r^2)-(s) \\ \\ (mx)/(n)=(t^2)/(r^2)-s \end{gathered}`

4. Since "n" is dividing on the left side, you must multiply to both sides of the equation by "n":

`\begin{gathered} (n)((mx)/(n))=((t^2)/(r^2)-s)(n) \\ \\ mx=(t^2n)/(r^2)-sn \end{gathered}`

5. The variable "m" is multiplying the variable "x", then you can divide both sides of the equation by "m":

`\begin{gathered} (mx)/(m)=((t^2n)/(r^2)-sn)/(m) \\ \\ x=(t^2n)/(r^2m)-(sn)/(m) \end{gathered}`

Therefore, the answer is:

- First, I divide both sides of the equation by "r", because it reverses the Multiplication on the left side that acts on the variable "x".

- Second, I square both sides of the equation, because the inverse operation of taking the square root, is squaring. Then, it reverses the square root on the left side that acts on the variable "x".

- Third, I subtract "s" from both sides of the equation, because that reverses the Addition that acts on the variable "x" on the left side of the equation.

- Fourth, I multiply to both sides of the equation by "n", because it reverses the Division on the left side that acts on the variable "x".

- Fifth, I divide both sides of the equation by "m", because it reverses the Multiplication on the left side that acts on the variable "x".