Question

How do you solve for $w$ in $2w-y=7w-2$?

Answer 1

Hint: $2w-y=7w-2$ is the given equation. We need to transfer all the terms with the variable $w$ to one side and remaining terms on another side. Now we need to solve the equation. As the equation is a linear equation, there are three types of methods to solve it. Those are the substitution method, graphing method, and elimination method. Here we can do the elimination method and find out the value.

Complete step-by-step solution:
The given equation is $2w-y=7w-2$. We need to simplify and solve the equation.
$\Rightarrow 2w-y=7w-2$
There are four terms in the equation. Two terms on the left-hand side and two terms on the right-hand side.
Now we should find the value of $w$. This can be done by changing all the terms to one side except the terms which have $w$.
Here the terms which have $w$ are 2w and 7w. So, we will shift 2w to the RHS such that we get 7w-2w and the result would be 5w.
Now, taking -2 to the LHS, and writing the equation, we have
$\Rightarrow 2-y=5w$
Now we need to divide everything with five so that the coefficient of $w$ will be one.
$\begin{align}
  & \Rightarrow 5w=2-y \\
 & \Rightarrow \dfrac{5w}{5}=\dfrac{2-y}{5} \\
\end{align}$
$\Rightarrow w=\dfrac{2-y}{5}$
Therefore the solution for $2w-y=7w-2$ is $\dfrac{2-y}{5}$.

Note: The equation given in the question is linear. Coefficient, variable, and constant will be there in the linear equation. In the linear equation, the variable will have the exponent one. In the linear equations, all the coefficients are real numbers and the coefficient of the higher exponent is not equal to zero. All the operations can be used in linear equations.