$$\left. \begin{array} { l } { \frac { 3 t + 1 } { 16 } - \frac { 2 t - 3 } { 7 } = \frac { t + 3 } { 8 } + \frac { 3 t - 1 } { 14 } } \\ { 4 ? } \end{array} \right.$$
$u=4$
$$7\left(3t+1\right)-16\left(2t-3\right)=14\left(t+3\right)+8\left(3t-1\right)$$
$$21t+7-16\left(2t-3\right)=14\left(t+3\right)+8\left(3t-1\right)$$
$$21t+7-32t+48=14\left(t+3\right)+8\left(3t-1\right)$$
$$-11t+7+48=14\left(t+3\right)+8\left(3t-1\right)$$
$$-11t+55=14\left(t+3\right)+8\left(3t-1\right)$$
$$-11t+55=14t+42+8\left(3t-1\right)$$
$$-11t+55=14t+42+24t-8$$
$$-11t+55=38t+42-8$$
$$-11t+55=38t+34$$
$$-11t+55-38t=34$$
$$-49t+55=34$$
$$-49t=34-55$$
$$-49t=-21$$
$$t=\frac{-21}{-49}$$
$$t=\frac{3}{7}$$
$$t=\frac{3}{7}$$ $$u=4$$
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