Question

Solve the equation. Check your solution.

$\mathbf{18}\mathbf{w}\mathbf{-}\mathbf{2}\mathbf{=}\mathbf{10}\mathbf{w}\mathbf{+}\mathbf{14}$

Short answer

The solution for the equation$18w-2=10w+14$is$w=2$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}18w-2=10w+14\\ \text{18}w-2-18w=10w+14-18w\text{[Substract18}w\text{fromeachside.]}\\ -2=14-8w\text{[Simplify.]}\\ -2-14=14-14-8w\text{[Subtract14fromeachside.]}\\ -16=-8w\text{[Simplify.]}\end{array}$

– Solve for w

Now, divide both sides of the equation by 8.

$\begin{array}{c}-\frac{16}{8}=-\frac{8w}{8}\\ w=2\end{array}$

Therefore, the solution of the equation is $w=2$.

– Check the solution 

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

$18w-2=10w+14$

Now, substitute and check the result.

$\begin{array}{c}18\left(2\right)-2=10\left(2\right)+14\\ 36-2=20+14\\ 34=34\end{array}$

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