Question
Solve the equation and check your result: $2y + \frac{5}{3} = \frac{{26}}{3} - y$
✓
Answer
$2y + \frac{5}{3} = \frac{{26}}{3} - y$
$2y + y = \frac{{26}}{3} - \frac{5}{3}$ ... [Transposing –y to $L.H.S$. and $\frac{5}{3}$ to $R.H.S]$
$\therefore 3y = \frac{{26 - 5}}{3}$
$\therefore 3y = \frac{{21}}{3}$
$\therefore 3y = 7$
$\therefore$ y = $\frac{7}{3}$ ... [Dividing both sides by $3$]
This is the required solution.
Verification
$L.H.S. = 2\left( {\frac{7}{3}} \right) + \frac{5}{3} = \frac{{14}}{3} + \frac{5}{3} = \frac{{14 + 5}}{3} = \frac{{19}}{3}$
$R.H.S. = \frac{{25}}{3} - \frac{7}{3} - = \frac{{26 - 7}}{3} = \frac{{19}}{3}$
Therefore, $L.H.S = R.H.S$
$2y + y = \frac{{26}}{3} - \frac{5}{3}$ ... [Transposing –y to $L.H.S$. and $\frac{5}{3}$ to $R.H.S]$
$\therefore 3y = \frac{{26 - 5}}{3}$
$\therefore 3y = \frac{{21}}{3}$
$\therefore 3y = 7$
$\therefore$ y = $\frac{7}{3}$ ... [Dividing both sides by $3$]
This is the required solution.
Verification
$L.H.S. = 2\left( {\frac{7}{3}} \right) + \frac{5}{3} = \frac{{14}}{3} + \frac{5}{3} = \frac{{14 + 5}}{3} = \frac{{19}}{3}$
$R.H.S. = \frac{{25}}{3} - \frac{7}{3} - = \frac{{26 - 7}}{3} = \frac{{19}}{3}$
Therefore, $L.H.S = R.H.S$
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