Question

How do you solve \[2(x - 1) + 3 = x - 3(x + 1)\]?

Answer 1

Hint: In the given problem we need to solve this for ‘x’. 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 ‘x’ terms one side and constants on the other side of the equation.

Complete step by step solution:
Given, \[2(x - 1) + 3 = x - 3(x + 1)\].
Firstly we expand the brackets in left hand and right hand side of the equation,
\[2x - 2 + 3 = x - 3x - 3\]
\[2x + 1 = x - 3x - 3\]
Taking ‘x’ common in the right hand side of the equation,
\[2x + 1 = x(1 - 3) - 3\]
\[2x + 1 = - 2x - 3\]
We transpose ‘1’ which is present in the left hand side of the equation to the right hand side of the equation by subtracting ‘1’ on the right hand side of the equation.
\[2x = - 2x - 3 - 1\]
Similarly we transpose ‘-2x’ to the left hand side by adding ‘2x’ on the left hand side
\[2x + 2x = - 3 - 1\]
Taking ‘x’ common we have,
\[x\left( {2 + 2} \right) = - 3 - 1\]
\[4x = - 4\]
Divide the by 4 on both sides of the equations,
\[x = - \dfrac{4}{4}\]
\[ \Rightarrow x = - 1\]. This is the required answer.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘x’ in the given problem.
\[2(x - 1) + 3 = x - 3(x + 1)\]
\[2( - 1 - 1) + 3 = - 1 - 3( - 1 + 1)\]
\[2( - 2) + 3 = - 1 - 3(0)\]
\[ - 4 + 3 = - 1 - 0\]
\[ - 1 = - 1\].
That is LHS=RHS. Hence the obtained is correct.
In the above we did the transpose of addition and subtraction. 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.