$$\frac{ x+2 }{ 5 } - \frac{ 2 }{ 4 } \leq \frac{ 4+2x }{ 5 }$$
$x\geq -\frac{9}{2}$
$$4\left(x+2\right)-5\times 2\leq 4\left(4+2x\right)$$
$$4x+8-5\times 2\leq 4\left(4+2x\right)$$
$$4x+8-10\leq 4\left(4+2x\right)$$
$$4x-2\leq 4\left(4+2x\right)$$
$$4x-2\leq 16+8x$$
$$4x-2-8x\leq 16$$
$$-4x-2\leq 16$$
$$-4x\leq 16+2$$
$$-4x\leq 18$$
$$x\geq \frac{18}{-4}$$
$$x\geq -\frac{9}{2}$$
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