Đáp án:
$$a) x=-\dfrac{375}{448}\\ b) x=-\dfrac{13}{15}; x=\dfrac{17}{15}\\ c) x=0;x=\dfrac{3}{4}\\ d) x=\dfrac{5}{21}.$$
Giải thích các bước giải:
$$a) \dfrac{8}{5}x-\dfrac{4}{3}x=\left(-\dfrac{5}{16}\right):1\dfrac{2}{5}\\ \Rightarrow \dfrac{24}{15}x-\dfrac{20}{15}x=-\dfrac{5}{16}:\dfrac{7}{5}\\ \Rightarrow \dfrac{4}{15}x=-\dfrac{5}{16}.\dfrac{5}{7}\\ \Rightarrow \dfrac{4}{15}x=-\dfrac{25}{112}\\ \Rightarrow x=-\dfrac{25}{112}: \dfrac{4}{15}\\ \Rightarrow x=-\dfrac{375}{448}$$
Vậy $$x=-\dfrac{375}{448}$$
$$b) \left(\dfrac{1}{5}-\dfrac{3}{2}x\right)^2=\dfrac{9}{4}\\ \Rightarrow \left(\dfrac{1}{5}-\dfrac{3}{2}x\right)^2=\left(\dfrac{3}{2}\right)^2\\ \Rightarrow \left|\dfrac{1}{5}-\dfrac{3}{2}x\right|=\dfrac{3}{2}\\ \circledast \dfrac{1}{5}-\dfrac{3}{2}x=\dfrac{3}{2}\\ \Rightarrow -\dfrac{3}{2}x=\dfrac{13}{10}\\ \Rightarrow x=-\dfrac{13}{15}\\ \circledast \dfrac{1}{5}-\dfrac{3}{2}x=-\dfrac{3}{2}\\ \Rightarrow -\dfrac{3}{2}x=-\dfrac{17}{10}\\ \Rightarrow x=\dfrac{17}{15}$$
Vậy $$x=-\dfrac{13}{15}; x=\dfrac{17}{15}$$
$$c) |2x-1|=\left|1-\dfrac{2}{3}x\right|\\ \circledast 2x-1=1-\dfrac{2}{3}x\\ \Rightarrow 2x+\dfrac{2}{3}x=1+1\\ \Rightarrow \dfrac{8}{3}x=2\\ \Rightarrow x=\dfrac{3}{4}\\ \circledast 2x-1=\dfrac{2}{3}x-1\\ \Rightarrow 2x-\dfrac{2}{3}x=-1+1\\ \Rightarrow \dfrac{4}{3}x=0\\ \Rightarrow x=0$$
Vậy $$x=0;x=\dfrac{3}{4}$$
$$d) 2\left(\dfrac{1}{3}-\dfrac{3}{5}x\right)-3\left(\dfrac{1}{6}+\dfrac{1}{5}x\right)=x-\dfrac{1}{2}\\ \Rightarrow \dfrac{2}{3}-\dfrac{6}{5}x-\dfrac{1}{2}-\dfrac{3}{5}x=x-\dfrac{1}{2}\\ \Rightarrow -\dfrac{6}{5}x-\dfrac{3}{5}x-x=-\dfrac{1}{2}-\dfrac{2}{3}+\dfrac{1}{2}\\ \Rightarrow -\dfrac{14}{5}x=-\dfrac{2}{3}\\ \Rightarrow x=\dfrac{5}{21}$$
Vậy $$x=\dfrac{5}{21}.$$
