$$\frac{ 5(3-x) }{ 4 } + \frac{ 3x+8 }{ 6 } =3(x+1)$$
$x=\frac{5}{9}\approx 0.555555556$
$$3\times 5\left(3-x\right)+2\left(3x+8\right)=36\left(x+1\right)$$
$$15\left(3-x\right)+2\left(3x+8\right)=36\left(x+1\right)$$
$$45-15x+2\left(3x+8\right)=36\left(x+1\right)$$
$$45-15x+6x+16=36\left(x+1\right)$$
$$45-9x+16=36\left(x+1\right)$$
$$61-9x=36\left(x+1\right)$$
$$61-9x=36x+36$$
$$61-9x-36x=36$$
$$61-45x=36$$
$$-45x=36-61$$
$$-45x=-25$$
$$x=\frac{-25}{-45}$$
$$x=\frac{5}{9}$$
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