Question

What is the value of x when \[2x + 3 = 3x - 4\]?

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.

Complete step-by-step solutions:
Given, \[2x + 3 = 3x - 4\].
We transpose ‘3’ which is present in the left hand side of the equation to the right hand side of the equation by subtracting ‘3’ on the right hand side of the equation.
\[2x = 3x - 4 - 3\]
Similarly we transpose 3x to the left hand side by subtracting 3x on the left hand side of the equation.
\[2x - 3x = - 4 - 3\]
\[ - x = - 7\]
\[ \Rightarrow x = 7\].
This is the required answer.

Thus the required answer is x=7.

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.
\[\Rightarrow 2x + 3 = 3x - 4\]
\[\Rightarrow 2(7) + 3 = 3(7) - 4\]
\[\Rightarrow 14 + 3 = 21 - 4\]
\[ \Rightarrow 17 = 17\].
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.