Question

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

Answer 1

We need to solve the equation shown below for x:

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

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

`\begin{gathered} (1)/(3)(2x)-(1)/(3)(1)=z \\ (2)/(3)x-(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} (2)/(3)x-(1)/(3)=z \\ (2)/(3)x=z+(1)/(3) \\ x=(z+(1)/(3))/((2)/(3)) \end{gathered}`

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

`\begin{gathered} x=(z)/((2)/(3))+((1)/(3))/((2)/(3)) \\ x=z*(3)/(2)+(1)/(3)*(3)/(2) \\ x=(3z)/(2)+(1)/(2) \\ x=(3z+1)/(2) \end{gathered}`

The final answer:

`x=(3z+1)/(2)`