Question

If $\dfrac{{\left( {2x - 1} \right)}}{3} = \left( {\dfrac{{\left( {x - 2} \right)}}{3}} \right) + 1$, then $x = $
A) $2$
B) $4$
C) $6$
D) $8$

Answer 1

Hint:
Shift the variables which are the same to any one side, and solve the equation for that variable.

Complete step by step solution:
Shift the variables of $x$onto left hand side,
$
   \Rightarrow \dfrac{{2x - 1}}{3} = \left( {\dfrac{{\left( {x - 2} \right)}}{3}} \right) + 1 \\
  Multiply\,the\,equation\,with\,3 \\
   \Rightarrow 3\left( {\dfrac{{2x - 1}}{3}} \right) = 3\left( {\dfrac{{\left( {x - 2} \right)}}{3}} \right) + 3 \\
   \Rightarrow 2x - 1 = x - 2 + 3 \\
   \Rightarrow 2x - 1 = x - 2 + 3 \\
   \Rightarrow x = 1 - 2 + 3 \\
   \Rightarrow x = 2 \\
 $

So, the value of $x$is $2$, Option A is correct.

Note:
When shifting the variable from one side to another side i.e. LHS to RHS or RHS to LHS the sign of the value and variable changes.