Giải các phương trình:

$$\begin{gathered} a) 3-4x(25-2x)=8x^2+x-300 \\ b) \frac{2(1-3x)}{5}-\frac{2+3x}{10}=7-\frac{8(2x+1)}{4} \\ c) \frac{5x+2}{5}-\frac{8x-1}{3}=\frac{4x+2}{5}-5 \\ d) \frac{3x+2}{2}-\frac{3x+1}{5}=2x+\frac{5}{3} \end{gathered}$$

Giải

a) $$\begin{gathered} 3-4x(25-2x)=8x^2+x-300 \\ \iff 3-100x+8x^2=8x^2+x-300\iff 101x=303\iff x=3\Rightarrow S=\left\{3\right\} \end{gathered}$$

b) quy đồng khử mẫu thì được $$\begin{gathered} 8(1-3x)-2(2+3x)=140-15(2x+1) \\ \iff -30x+4=-20x+125\iff 0x=121 \end{gathered}$$

vậy phương trình vô nghiệm

c) $$\begin{gathered} \frac{5x+2}{6}-\frac{8x-1}{3}=\frac{4x+2}{5}-5 \\ \iff 5(5x+2)-10(8x-1)=6(4x+2)-150 \\ \iff -55x+20=24x-138\iff 79x=158\iff x=2 \end{gathered}$$

d) $$\begin{gathered} \frac{3x+2}{2}-\frac{3x+1}{6}=2x+\frac{5}{3}\iff 3(3x+2)-(3x+1)=12x+10 \\ \iff 6x+5=12x+10\iff x=-\frac{5}{6} \end{gathered}$$