$$x- \frac{ 1+2x }{ 4 } \geq \frac{ 1-3x }{ 2 }$$
$x\geq \frac{3}{8}$
$$4x-\left(1+2x\right)\geq 2\left(1-3x\right)$$
$$4x-1-2x\geq 2\left(1-3x\right)$$
$$2x-1\geq 2\left(1-3x\right)$$
$$2x-1\geq 2-6x$$
$$2x-1+6x\geq 2$$
$$8x-1\geq 2$$
$$8x\geq 2+1$$
$$8x\geq 3$$
$$x\geq \frac{3}{8}$$
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