Question

Solve the equation $c=\frac{2}{a}+\frac{b}{5}$for the variable $a$.

Short answer

The required expression is$a=\frac{10}{5c-b}$.

Step-by-step solution

Given information

The equation is given as$c=\frac{2}{a}+\frac{b}{5}$to find the expression.

Solve the given equation

Apply the algebraic operations to find the required expression for the given equation.

• Subtract $\frac{b}{5}$into both sides of the given equation and solve for $a$.

$\begin{array}{rcl}c& =& \frac{2}{a}+\frac{b}{5}\\ c-\frac{b}{5}& =& \frac{2}{a}+\frac{b}{5}-\frac{b}{5}\\ c-\frac{b}{5}& =& \frac{2}{a}\\ \frac{5c-b}{5}& =& \frac{2}{a}\\ \frac{5}{5c-b}& =& \frac{a}{2}\\ a& =& \frac{5\times 2}{5c-b}\\ a& =& \frac{10}{5c-b}\end{array}$