Solve the following equation.
$t - (2 t + 5) - 5 (1 - 2 t) = 2 (3 + 4 t) - 3 (t - 4)$ .

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Solution

$t - (2 t + 5) - 5 (1 - 2 t) = 2 (3 + 4 t) - 3 (t - 4)$
$\Rightarrow t - 2 t - 5 - 5 + 10 t = 6 + 8 t - 3 t + 12$ [Using distributive property]
$\Rightarrow 9 t - 10 = 5 t + 18$ [Combining like terms]
$\Rightarrow 9 t - 5 t = 18 + 10$ [Transposed $5 t$ and $- 10$ to other side]
$\Rightarrow 9 t - 5 t = 28$
$\Rightarrow 4 t = 28$
$\Rightarrow t = \frac{28}{4}$ [Transposed $4$ to other side]
$\Rightarrow t = 7$

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