Question

How do you solve the linear equation $\dfrac{1}{2}x - 1 = 4$?

Answer 1

Hint: First of all, take the 1 from subtraction in the left hand side to addition in RHS, then simplify the calculations on the RHS. Then, just multiply the equation by 2 to get the answer.

Complete step-by-step solution:
We are given that we are required to solve $\dfrac{1}{2}x - 1 = 4$.
In the above equation, after taking 1 from subtraction from the left hand side to addition in the right hand side, we will then obtain the following equation as:-
$ \Rightarrow \dfrac{1}{2}x = 4 + 1$
Simplifying the calculations on the right hand side of the above equation, we will then obtain the following equation as:-
$ \Rightarrow \dfrac{1}{2}x = 5$
Multiplying both the sides of the above equation by 2, we will then obtain the following equation as:-
$ \Rightarrow x = 5 \times 2$
Simplifying the calculations on the right hand side of the above equation, we will then obtain the following equation as::-
$ \Rightarrow x = 10$
Thus, we have the required answer as 10 .

Note: The students must note that we did multiply the equation by 2 and could do that because we were sure that 2 can never be equal to 0. We can never multiply or divide an equation by such a variable which has even the slightest possibility of being equal to 0.
The students must know that we require as many equations as many numbers of unknown variables we do have. Here, we just had an unknown variable x and we had one equation given with us, therefore, we could easily solve it and thus, have the required answer.
Here, we have basically a linear equation with us. Linear equation is an equation with degree 1.
If we would have had more than one variable, we could just find one variable in terms of another variable, then we would have to assume one as a free variable.