$$\frac{ 3x+1 }{ 4 } - \frac{ 1 }{ 3 } \leq \frac{ 2 }{ 15 } (x+3)+ \frac{ 4(1-x) }{ 3 }$$
$x\leq \frac{109}{117}$
$$15\left(3x+1\right)-20\leq 8\left(x+3\right)+20\times 4\left(1-x\right)$$
$$45x+15-20\leq 8\left(x+3\right)+20\times 4\left(1-x\right)$$
$$45x-5\leq 8\left(x+3\right)+20\times 4\left(1-x\right)$$
$$45x-5\leq 8x+24+20\times 4\left(1-x\right)$$
$$45x-5\leq 8x+24+80\left(1-x\right)$$
$$45x-5\leq 8x+24+80-80x$$
$$45x-5\leq 8x+104-80x$$
$$45x-5\leq -72x+104$$
$$45x-5+72x\leq 104$$
$$117x-5\leq 104$$
$$117x\leq 104+5$$
$$117x\leq 109$$
$$x\leq \frac{109}{117}$$
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