Question

Solve the equation. Check your solution.

$\mathbf{3}\mathbf{n}\mathbf{-}\mathbf{40}\mathbf{+}\mathbf{2}\mathbf{n}\mathbf{=}\mathbf{15}$

Short answer

The solution for the equation$3n-40+2n=15$is$n=11$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variables.

$\begin{array}{c}3n-40+2n=15\\ 3n-40+2n+40=15+40\\ 3n+2n=15+40\\ 5n=55\end{array}$

– Solve for n

Now, divide both sides of the equation by 5.

$\begin{array}{c}\frac{5n}{5}=\frac{55}{5}\\ n=11\end{array}$

Therefore, the solution of the equation is $n=11$.

– Check the solution 

To check the solution, write the original equation and substitute the value of n.

$3n-40+2n=15$

Now, substitute $n=11$and check the result.

$\begin{array}{c}3\left(11\right)-40+2\left(11\right)=15\\ 33-40+22=15\\ 55-40=15\\ 15=15\end{array}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.