Chapter MH, Problem 9PP

Solution

Interpretation: The variable y in the given equation needs to be isolated.

  $z=x\left(4+2y\right)$

Concept Introduction: The variable is isolated to determine its value in the equation. In this, the variable that needs to be isolated is alone on one side of the equation, and the rest of the variables and numbers are on the right.

This can be done by simply adding, subtracting, multiplying, and dividing something into both sides of the equation.

  $y=\frac{1}{2}\left(\frac{z}{x}-4\right)$

The given equation is as follows:

  $z=x\left(4+2y\right)$

Here, variable y needs to be isolated.

To do so, divide both sides of the equation by x .

  $\frac{z}{x}=\frac{\cancel{x}\left(4+2y\right)}{\cancel{x}}$

Or,

  $\frac{z}{x}=4+2y$

Subtract both sides of the equation by 4.

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

Now, divide both sides of the equation by 2.

  $\frac{1}{2}\left(\frac{z}{x}-4\right)=\frac{2y}{2}$

Thus,

  $y=\frac{1}{2}\left(\frac{z}{x}-4\right)$

Thus, the variable y can be isolated as follows:

  $y=\frac{1}{2}\left(\frac{z}{x}-4\right)$