Question

If $2y + \dfrac{5}{3} = \dfrac{{26}}{3} - y$, then $y = $
A) $1$
B) $\dfrac{2}{3}$
C) $\dfrac{6}{5}$
D) $\dfrac{7}{3}$

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 $y$ onto left hand side,
$
   \Rightarrow 2y + \dfrac{5}{3} = \dfrac{{26}}{3} - y \\
   \Rightarrow 2y + y = \dfrac{{26}}{3} - \dfrac{5}{3} \\
\text{Adding the terms involving y and on the right hand side taking LCM} \\
   \Rightarrow 3y = \dfrac{{26 - 5}}{3} \\
   \Rightarrow 3y = \dfrac{{21}}{3} \\
\text{on the right hand side diving 21 by 3} \\
   \Rightarrow 3y = 7 \\
\text{dividing whole equation by 3} \\
   \Rightarrow y = \dfrac{7}{3} \\
 $

So, the value of $y$ is $\dfrac{7}{3}$, Option D 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.