Question

How do you solve \[3-2x=8+2x\] ?

Answer 1

Hint: For these types of problems we can see clearly that there is only one unknown parameter and the power of the unknown parameter which is ‘x’, is $1$ . So this equation can in general be described as a polynomial equation with degree one. The general form of these types of degree one equations is,
\[ax=b\]
Where ‘a’ is the index, ‘x’ is the unknown parameter and ‘b’ is a constant. Now, for problems like these, what we need to do is transform the equation and bring all the like terms of the equation to one side and all the other constant to the other side, thereby forming an equation which looks similar to that of the general form, so that the evaluation of the unknown parameter becomes easy.

Complete step by step solution:
Now, we start off with the solution of the problem and write it as,
The left hand side of the equation is basically a linear equation and so is the right hand side. Now, we bring all the like terms of this given equation on one side and then evaluate it further. We hence bring all the ‘x’ terms to the left hand side and all the constants to the right hand side. Rearranging all the terms, we get,
\[-4x=5\]
Now, if we take a closer look at our intermediate equation then we will easily find that this equation is very similar to that of the general form of linear equation. Thus, comparing that, we can easily find out the value of the unknown parameter ‘x’ as,
\[x=-\dfrac{5}{4}\]

Note: For problems like these we need to be thorough about the concepts of linear equations. We can also solve this type of problems using the theory of graphs. In graphs, we consider both the sides of the linear equation to be a function and then plot them on the graph paper. Hence we get two straight lines if we plot both the sides of the equation. The point of intersection of these two straight lines, gives us our required value of the unknown parameter ‘x’.