Question

Solve the following equations by systematic method:
\[3x-5=7\]

Answer 1

Hint: Consider the expression, by rule of systematic method for addition and division, solve the expression for x. We need to get x by itself on the LHS of the equation.

Complete step-by-step answer:
The systematic method is done with the working of a balance i.e. both the LHS and RHS has to be the same. For example, we can say that, if equal weights are put in the two pans, we can observe that the 2 pans remain in balance.
If we remove equal weights from both the pans, we find that the pan remains in balance.
Thus multiplying a number by 5 means adding it 5 times and dividing a number by 3 means than to subtracting the same number 3 times from it. Thus the pan remains still.
We have been given, \[3x-5=7-(1)\]
By rule of systematic method for addition, we can add the same number to both sides of the equation.
In order to solve this equation, we need to get X by itself on LHS. Thus first let us add 5 on both sides of equation (1).
\[3x-5+5=7+5\]
Hence we get, \[3x=12-(2)\].
Now by the rule of systematic method for division, we can divide both sides of the equation by the same non – zero number. So let us divide 3 on both sides of equation (2).
\[\therefore \dfrac{3x}{3}=\dfrac{12}{3}\]
Thus we get, \[x=4\].
Hence, we solved the equation using systematic methods and \[x=4\].

Note: There are rules of systematic method for subtraction and multiplication, where this is done on both sides of the expression. We can also solve the equation in a normal way to confirm the answer.
\[3x-5=7\]
\[\begin{align}
  & \therefore 3x=7+5=12\Rightarrow 3x=12 \\
 & \therefore x=\dfrac{12}{3}=4 \\
\end{align}\]