Question

1/3 (2x - 1) = z for x

Answer 1

We need to solve the equation shown below for x:

$\frac{1}{3}(2x-1)=z$

Using distributive propery, a(b - c) = ab - ac , we can simplify the left hand side:

$\begin{gathered} \frac{1}{3}(2x)-\frac{1}{3}(1)=z \\ \frac{2}{3}x-\frac{1}{3}=z \end{gathered}$

We isolate the term with x and then divide the other side by 2/3 to get x = something...

$\begin{gathered} \frac{2}{3}x-\frac{1}{3}=z \\ \frac{2}{3}x=z+\frac{1}{3} \\ x=\frac{z+\frac{1}{3}}{\frac{2}{3}} \end{gathered}$

To simplify it (reduce), we can divide both terms by (2/3) and simplify. Shown below:

$\begin{gathered} x=\frac{z}{\frac{2}{3}}+\frac{\frac{1}{3}}{\frac{2}{3}} \\ x=z\times\frac{3}{2}+\frac{1}{3}\times\frac{3}{2} \\ x=\frac{3z}{2}+\frac{1}{2} \\ x=\frac{3z+1}{2} \end{gathered}$

The final answer:

$x=\frac{3z+1}{2}$