Question

Solve the equation. Check your solution.

$9n+64=-144+17n$

Short answer

The solution for the equation is $n=26$.

Step-by-step solution

Step 1.  Apply the concept of Linear Equation

In this type of equation, simply use the tools of mathematical operations like addition, subtraction, multiplication or division to eliminate the numbers in the equation and also maintaining the equality by using the proper numbers and get the result.

Step 2.  Find the value of n by solving the inequality

Since, the equation is $9n+64=-144+17n$.

Here, to simplify this equation, Take the variable in left hand side and the numbers in right hand side and do mathematical operations to get the solution.

$\begin{array}{l}9n+64=-144+17n\\ 9n-17n=-144-64\\ \cancel{-}8n=\cancel{-}208\\ n=\frac{208}{8}\\ n=26\end{array}$

Step 3.  Check the equation to verify the equality

Since, the solution is, $n=26$and the equation is $9n+64=-144+17n$.

So,

Put $n=26$in equation,

$\begin{array}{l}LeftHandSide:\\ =9n+64\\ =9\left(26\right)+64\\ =234+64\\ =298\\ RightHandSide\\ =-144+17n\\ =-144+17\left(26\right)\\ =-144+442\\ =298\end{array}$

It holds the equation.

So, the solution $n=26$correctly holds the equation.