Chapter 2.4, Problem 29P

Solve each equation. If the equation is an identity, write identity. If it has no solution, write no solution.

$\frac{3}{8}f+\frac{1}{2}=6\left(\frac{1}{16}f-3\right)$

To determine

To solve an equation $\frac{3}{8}f+\frac{1}{2}=6\left(\frac{1}{16}f-3\right)$ and write if the equation is an identity.

Answer to Problem 29P

The given equation $\frac{3}{8}f+\frac{1}{2}=6\left(\frac{1}{16}f-3\right)$ has no solutions.

Explanation of Solution

Given information :

Given equation $\frac{3}{8}f+\frac{1}{2}=6\left(\frac{1}{16}f-3\right)$

As we have $-6\left(-p+8\right)=-6p+12$

  $\begin{array}{l}\Rightarrow \frac{3}{8}f=\frac{6}{16}f-18-\frac{1}{2}\\ \Rightarrow \frac{3}{8}f=\frac{3}{8}f+\left(\frac{-36-1}{2}\right)\\ \Rightarrow \frac{3}{8}f-\frac{3}{8}f=\frac{-37}{2}\\ \Rightarrow 0=-18.5\end{array}$

Which is not possible,

Hence, the given equation $\frac{3}{8}f+\frac{1}{2}=6\left(\frac{1}{16}f-3\right)$ has no solutions.