Question

Solve the equation. Check your solution.$\mathbf{13}\mathbf{=}\mathbf{2}\mathbf{y}\mathbf{-}\mathbf{3}(\mathbf{y}\mathbf{+}\mathbf{4})$

Short answer

The solution for the equation $13=2y-3(y+4)$is localid="1650416876257" $y=-25$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}13+12=2y-3y-12+12\\ 25=2y-3y\\ -y=25\end{array}$

– Solve for y

Now, multiply both sides of the equation by -1.

$\begin{array}{c}-y(-1)=25(-1)\\ y=-25\end{array}$

Therefore, the solution of the equation is$y=-25$.

– Check the solution 

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

$13=2y-3(y+4)$

Now, substitute $y=25$and check the result.

$\begin{array}{c}13=2(-25)-3((-25)+4)\\ 13=-50-3(-21)\\ 13=-50+63\\ 13=13\end{array}$

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