Question

Solve the equation and check the solution.

$3w+14=7w+2$

Short answer

The solution is $w=3$.

Step-by-step solution

Step 1- Consider the equation.

Consider the equation $3w+14=7w+2$.

Separate the coefficient of on one side of the equation.

Step 2- Step description.

$\begin{array}{l}3w+14=7w+2\\ 3w-7w=2-14\\ -4w=-12\end{array}$

Step 3- Step description.

Divide both sides of the equation by $-4$.

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

Therefore, the solution is $w=3$.

Step 4- Verify the solution.

Substitute $w=3$in the equation and simplify as follows:

$\begin{array}{l}3w+14=7w+2\\ 3\left(3\right)+14=7\left(3\right)+2\\ 9+14=21+2\\ 23=23\end{array}$

Since the left-hand side of the equation is equal to the right-hand side of the equation, therefore, the solution is $w=3$.