Question

Solve
\[5x - 6 = 4x - 2\]

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 to bring like terms together and isolate the variable (or the unknown quantity). That is, we group the ‘x’ terms on one side and constants on the other side of the equation.

Complete step-by-step answer:
Given, \[5x - 6 = 4x - 2\].
We transpose ‘-6’ which is present on the left-hand side of the equation to the right-hand side of the equation by adding ‘6’ on the right-hand side of the equation.
\[5x = 4x - 2 + 6\]
Now similarly we transpose 4x to the left-hand side of the equation by subtracting 4x on the left-hand side of the equation.
\[5x - 4x = - 2 + 6\]
Now we have separated the variable term and the constant term,
\[ \Rightarrow x = 4\].
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. If LHS is equal to RHS then the obtained answer is correct.
\[5x - 6 = 4x - 2\]
\[5(4) - 6 = 4(4) - 2\]
\[20 - 6 = 16 - 2\]
Simplifying we have,
\[ \Rightarrow 14 = 14\].
That is LHS=RHS. 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.