Question

Find the value of the variable.

$\left(4f+5\right)+\left(5f+40\right)=180$

Short answer

The value of the variable is $\mathit{f}\mathbf{=}\mathbf{15}$.

Step-by-step solution

Step 1. Combine the like terms.

First remove all the brackets and combine the like terms.

$\begin{array}{r}\left(4f+5\right)+\left(5f+40\right)=180\\ 4f+5+5f+40=180\\ 9f+45=180\end{array}$

Step 2. Subtract 45. 

To find the value of variable f in the equation $9f+45=180$, subtract 45 from both sides of the equation.

$\begin{array}{l}9f+45-45=180-45\\ 9f=\text{135}\end{array}$

Step 3. Divide by 9.

Divide both sides of the equation $9f=\text{135}$by 9 and cancel the common factors of 9 on both sides.

$\begin{array}{l}\frac{9f}{9}=\frac{\text{135}}{9}\\ f=\frac{15\times 9}{9}\\ f=15\end{array}$

Step 4. Verify the value.

In order to verify the value of f, substitute 15 for into the equation$\left(4f+5\right)+\left(5f+40\right)=180$.

$\begin{array}{l}\left(4\times 15+5\right)+\left(5\times 15+40\right)=180\\ \left(60+5\right)+\left(75+40\right)=180\\ 65+115=180\\ 180=180\text{True}\end{array}$

Hence, the value of the variable is $f=15$.