$$\frac{5t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t$$
$t = \frac{26}{19} = 1\frac{7}{19} \approx 1.368421053$
$$3\left(5t-2\right)-4\left(2t+3\right)=8-12t$$
$$15t-6-4\left(2t+3\right)=8-12t$$
$$15t-6-8t-12=8-12t$$
$$7t-6-12=8-12t$$
$$7t-18=8-12t$$
$$7t-18+12t=8$$
$$19t-18=8$$
$$19t=8+18$$
$$19t=26$$
$$t=\frac{26}{19}$$
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