Question

The solution of the linear equation \[1 - 4x = - 11\] is _______
A) \[x = 2\]
B) \[x = 3\]
C) \[x = - 3\]
D) \[x = 4\]

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. We can also solve this by substituting each option in the given linear equation. If LHS is equal to RHS then the substituted value is correct.

Complete step by step solution:
Given,
\[1 - 4x = - 11\]
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.
\[ - 4x = - 11 - 1\]
\[ - 4x = - 12\]
Now we transpose the \[ - 4\] to the right hand side of the equation by dividing \[ - 4\] on the right hand side of the equation.
\[x = \dfrac{{ - 12}}{{ - 4}}\]
On dividing we have,
\[ \Rightarrow x = 3\]. This is the required answer.
Hence the correct option is (B).

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.
\[1 - 4x = - 11\]
\[1 - 4(3) = - 11\]
\[1 - 12 = - 11\]
\[ \Rightarrow - 11 = - 11\]. Hence the obtained answer 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.