Question

How do you solve \[2(w - 1) + 4 = 4(w + 1)\] ?

Answer 1

Hint: In the given problem we need to solve this for ‘w’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘w’ terms one side and constants on the other side of the equation. ‘w’ is the unknown term that we need to find.

Complete step-by-step answer:
Given \[2(w - 1) + 4 = 4(w + 1)\] .
To solve this we expand the brackets which are present in the left and right hand side of the equation.
That is we have,
 \[ \Rightarrow 2w - 2 + 4 = 4w + 4\]
Adding the constant that are present in the left hand side of the equation we get,
 \[ \Rightarrow 2w + 2 = 4w + 4\] .
We transpose ‘2’ which is present in the left hand side of the equation to the right hand side of the equation by subtracting ‘2’ on the right hand side e get,
 \[ \Rightarrow 2w = 4w + 4 - 2\]
Similarly we transpose \[4w\] , which is present in the right hand side of the equation to the left hand side of the equation by subtracting \[4w\] on the left hand side of the equation.
 \[ \Rightarrow 2w - 4w = 4 - 2\]
Taking ‘w’ common we have
 \[ \Rightarrow w\left( {2 - 4} \right) = 4 - 2\]
 \[ \Rightarrow - 2w = 2\]
Dividing \[ - 2\] on both side of the equation we have,
 \[ \Rightarrow w = \dfrac{2}{{ - 2}}\]
 \[ \Rightarrow w = - 1\] . This is the required answer.
So, the correct answer is “w = - 1”.

Note: We can check if the answer is correct or not. To check all we need to do is substitute the value of ‘w’ in the given problem we have,
 \[2\left( { - 1 - 1} \right) + 4 = 4\left( { - 1 + 1} \right)\]
 \[2\left( { - 2} \right) + 4 = 4\left( 0 \right)\]
 \[ - 4 + 4 = 4\left( 0 \right)\]
 \[ \Rightarrow 0 = 0\] . Hence, the obtained answer is correct.
 If we want to transpose the addition number to any side of the equation we subtract it with the same number on both sides of the equation. Similarly if we want to transpose the negative number to any side of the equation we add with the same number on both sides of the equation. Similarly if we have multiplication we use division to transpose. If we have division we use multiplication to transpose. Follow the same procedure for these kinds of problems.