Question

Solve the equation. Check your solution.

$\mathbf{114}\mathbf{+}\mathbf{5}\mathbf{y}\mathbf{=}\mathbf{50}\mathbf{-}\mathbf{4}\mathbf{y}$

Short answer

The solution for the equation$\mathbf{1}14+5y=50-4y$ is$y=4$ .

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}\mathbf{1}14+5y=50-4y\\ 14+5y-5y=50-4y-5y\text{[Substract5yfromeachside.]}\\ 14=50-9y\text{[Simplify.]}\\ 14-50=50-9y-50\text{[Subtract50fromeachside.]}\\ -36=-9y\text{[Simplify.]}\end{array}$

– Solve for y

Now, divide both sides of the equation by 9.

$\begin{array}{c}-\frac{36}{9}=-\frac{9y}{9}\\ y=4\end{array}$

Therefore, the solution of the equation is$y=4$ .

– Check the solution 

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

$\mathbf{1}14+5y=50-4y$

Now, substitute $y=4$and check the result.

$\begin{array}{c}14+5\left(4\right)=50-4\left(4\right)\\ 14+20=50-16\\ 34=34\end{array}$

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