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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 250 (page 695)

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

Short Answer

Expert verified

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

Step by step solution

01

Given information

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

02

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 $a$ .

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

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