Question

Solve the equation and check the solution.

$5y+4=2\left(y-4\right)$

Short answer

The solution is $y=-4$.

Step-by-step solution

Step 1- Consider the equation.

Consider the equation $5y+4=2\left(y-4\right)$.

Simplify the right-hand side of the equation and thus separate the terms of the coefficient of y on one side of the equation.

Step 2- Step description.

$\begin{array}{l}5y+4=2\left(y-4\right)\\ 5y+4=2y-8\\ 5y-2y=-8-4\\ 3y=-12\end{array}$

Step 3- Step description.

Divide both sides of the equation by 3.

$\begin{array}{l}3y=-12\\ y=\frac{-12}{3}\\ y=-4\end{array}$

Therefore, the solution is $y=-4$.

Step 4- Verify the solution.

Substitute $y=-4$in the equation and simplify as follows:

$\begin{array}{l}5y+4=2\left(y-4\right)\\ 5\left(-4\right)+4=2\left(-4-4\right)\\ -20+4=2\left(-8\right)\\ -16=-16\end{array}$

Since the left-hand side of the equation is equal to the right-hand side of the equation, therefore, the solution is $y=-4$.