Question

How do you solve $\dfrac{1}{2}x - 2 = 2( - x + 1)$?

Answer 1

Hint: We will first open up the brackets in the right hand side and then bring on all the terms with x on one side that is on the left hand side and all the constant terms on the right hand side and then just club them.

Complete step-by-step solution:
We are given that we are required to solve $\dfrac{1}{2}x - 2 = 2( - x + 1)$.
Let us open up the brackets in the right hand side to obtain the following expression:-
$ \Rightarrow \dfrac{1}{2}x - 2 = - 2x + 2$
Taking 2x from subtraction in the right hand side to addition in left hand side, we will then obtain the following equation:-
$ \Rightarrow \dfrac{1}{2}x + 2x - 2 = 2$
Now, we will take the 2 from subtraction in the left hand side to addition in right hand side to obtain the following equation:-
$ \Rightarrow \dfrac{1}{2}x + 2x = 2 + 2$
Simplifying by clubbing the like terms on the right hand side of the above equation, we will obtain:-
$ \Rightarrow \dfrac{1}{2}x + 2x = 4$
Taking x common from the left hand side to obtain the following equation:-
$ \Rightarrow \left( {\dfrac{1}{2} + 2} \right)x = 4$
Now, taking the least common multiple, we will then obtain the following equation:-
$ \Rightarrow \left( {\dfrac{{1 + 4}}{2}} \right)x = 4$
Simplifying the left hand side of the above equation, we will then obtain the following equation:-
$ \Rightarrow \dfrac{5}{2}x = 4$
Now, we will multiply both sides of the above equation by 2 to obtain the following equation:-
$ \Rightarrow 5x = 8$
Now, we will divide both sides of the above equation by 5 to obtain the following equation:-
$ \Rightarrow x = \dfrac{8}{5}$
Thus, we have the required answer.

Note: The students must note that while opening up the brackets, we did use the distributive property of real numbers which state that: a ( b + c ) = ab + ac
Replacing a by 2, b by – x and c by 1, we will get: 2 (-x + 1) = -2x + 2
Thus we used this property in the beginning of our solution.
Also remember that we divide and multiply the equations by some number in a few steps, we can only do that with a non – zero number, because if we multiply by zero, the both sides become zero which does not make any sense.