Question

How do you solve \[3-2y=2\left( 3y-2 \right)-5y\] ?

Answer 1

Hint: These types of problems are pretty straight forward and are very easy to solve. For problems like these we need to find the value of the unknown parameter. In this given problem, we have a linear equation in ‘y’, the degree of ‘y’ here is one, and so this equation is nothing but a simple demonstration of a polynomial with degree one and we need to find the value of ‘y’. The general form of these types of degree one equations or polynomial is,
\[ay=b\]
Here ‘a’ is the index, ‘y’ is the unknown parameter and ‘b’ is a given constant. For our given problem, we rearrange our equation by shifting all the like terms to one side in such a way that the given equation becomes similar to our general linear equation. Doing so, solving such types of problems becomes very easy.

Complete step by step solution:
Now, we start off with the solution of the problem and write it as,
We first need to evaluate the right hand side of our equation by multiplying the terms and removing the brackets. After this, our equation transforms to,
\[3-2y=6y-4-5y\]
Now, we bring all the like terms, or the terms which have ‘y’ to the left side of our equation and the constants to the right hand side of the equation. Doing so we get,
\[\begin{align}
  & \Rightarrow -6y+5y-2y=-4-3 \\
 & \Rightarrow -3y=-7 \\
\end{align}\]
We can now clearly observe that our above equation looks similar to that of the general linear equation with one variable. We can now evaluate the value of ‘y’ from it as,
\[\Rightarrow y=\dfrac{7}{3}\]

Note: Since the given problem is of linear equations with one variable, we need to be very thorough with our knowledge of linear equations. This is also an alternate solution to these type of problems, i.e. using graphs. In such methods, we write both the sides of the equation as a function and plot them on the graph paper. Intersection point of the two straight lines plotted gives us our required answer.