Question

Solve each equation. Check your solution.

$\frac{3}{5}f+24=4-\frac{1}{5}f$

Short answer

The solution of the given equation is $f=-25$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$\frac{3}{5}f+24=4-\frac{1}{5}f$”.

Step 2. Solve the given equation.

Solving,

$\frac{3}{5}f+24=4-\frac{1}{5}f$ (Given equation)

$\frac{3}{5}f+24+\frac{1}{5}f=4-\frac{1}{5}f+\frac{1}{5}f$ (Add $\frac{1}{5}f$to both sides)

$\frac{4}{5}f+24=4$ (Simplify)

$\frac{4}{5}f+24-24=4-24$ (Subtract 24 from both sides)

$\frac{4}{5}f=-20$ (Simplify)

$\frac{4}{5}f\times \frac{5}{4}=-20\times \frac{5}{4}$ (Multiply both sides by $\frac{5}{4}$)

$f=-25$ (Simplify)

So, $f=-25$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $f=-25$in the given equation $\frac{3}{5}f+24=4-\frac{1}{5}f$to get,

$\begin{array}{l}\frac{3}{5}\left(-25\right)+24=4-\frac{1}{5}\left(-25\right)\\ 3\left(-5\right)+24=4-\left(-5\right)\\ -15+24=4+5\\ 9=9\end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.