Question

Solve the following equations .

$\frac{y}{2} - \frac{3y}{4} + \frac{5y}{6} = 21$
next question
$5(x - 2) + (x - 3) = 2(2x + 1) - 9$
next question
$\frac{n - 1}{2} - \frac{n - 2}{3} = \frac{n - 4}{7}$
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Answer 1

$\frac{y}{2} - \frac{3y}{4} + \frac{5y}{6} = 21$

$\frac{6y - 9y + 10y}{12} = 21$

$- 3y + 10y = 21 \times 12 \\ 7y = 252 \\ y = \frac{252}{7} \\ \\ y = 36$

Next question

$5( x- 2) + (x - 3) = 2(2x + 1) - 9 \\ 5x - 10 + x - 3 = 4x + 2 - 9\\ 6x - 13 = 4x - 7 \\ 6x - 4x = - 7 + 13 \\ 2x = 6 \\ x = \frac{6}{2} \\ x = 3$

Next question

$\frac{n - 1}{2} - \frac{n - 2}{3} = \frac{n - 4}{7} \\ \\ \frac{3n - 3 - (2n - 4)}{6} = \frac{n - 4}{7} \\ \\ \frac{3n - 3 - 2n + 4}{6} = \frac{n - 4}{7} \\ \\ \frac{n - 1}{6} = \frac{n - 4}{7} \\ \\ 7(n - 1) = 6(n - 4) \\ 7n - 7 = 6n - 24 \\ 7n - 6n = - 24 + 7 \\ n = - 17$