[tex]\it a)\ \ 1-4x\geq2x-7 \Rightarrow 1+7\geq2x+4x \Rightarrow 8\geq6x \Rightarrow 6x\leq8|_{:2} \Rightarrow \\ \\ \Rightarrow 3x\leq4|_{:3} \Rightarrow x\leq\dfrac{4}{3} \Rightarrow x\in\Big(-\infty,\ \dfrac{4}{3}\Big]\\ \\ \\ b)\ \ \dfrac{x+1}{3}-\dfrac{x}{6}\leq-1|_{\cdot6} \Rightarrow 2x+2-x\leq-6|_{-2} \Rightarrow x\leq-8 \Rightarrow x\in(-\infty,\ -8][/tex]
[tex]\it c)\ \ \dfrac{1-3x}{4}+\dfrac{x}{8}\geq-x|_{\cdot8} \Rightarrow 2-6x+x\geq-8x \Rightarrow 2-5x\geq-8x|_{+5x} \Rightarrow \\ \\ \Rightarrow 2\geq-3x|_{\cdot(-1)} \Rightarrow -2\leq3x \Rightarrow 3x\geq-2|_{:3} \Rightarrow x\geq-\dfrac{2}{3} \Rightarrow x\in\Big[-\dfrac{2}{3},\ \infty\Big)[/tex]
[tex]\it d)\ \ x-2\geq\dfrac{2x-3}{3}|_{\cdot3} \Rightarrow 3x-6\geq2x-3 \Rightarrow 3x-2x\geq-3+6 \Rightarrow \\ \\ \Rightarrow x\geq3 \Rightarrow x\in\Big[3,\ \infty\Big)[/tex]
