Question

Solve the equation. Check your solution.

$\mathbf{-}\mathbf{11}\mathbf{y}\mathbf{+}\mathbf{32}\mathbf{=}\mathbf{104}\mathbf{-}\mathbf{5}\mathbf{y}$

Short answer

The solution for the equation $-11y+32=104-5y$ is $y=-12$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}-11y+32=104-5y\\ -11y+5y+32=104-5y+5y\left(\text{add5ytobothsides}\right)\\ -6y+32=104\left(\text{simplify}\right)\\ -6y+32-32=104-32\left(\text{subtract32frombothsides}\right)\\ -6y=72\left(\text{simplify}\right)\end{array}$

– Solve for y

Now, divide both sides of the equation by -6.

$\begin{array}{c}\frac{-6y}{-6}=\frac{72}{-6}\\ y=-12\end{array}$

Therefore, the solution of the equation is $y=-12$.

– Check the solution 

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

$-11y+32=104-5y$

Now, substitute $y=-12$ and check the result.

$\begin{array}{c}-11\left(-12\right)+32=104-5\left(-12\right)\\ 132+32=104+60\\ 164=164\end{array}$

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