Thu gọn biểu thức

a) $\text{M=}\frac{{\mathrm{x}}^2+\left|4\mathrm{x}-1\right|-\left|2\mathrm{x}+8\right|-1}{\mathrm{x}+4}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{khi}\mathrm{\hspace{0.17em}}\mathrm{x}\ge \frac{1}{4};$ 

b) $\mathrm{N}=-8{\mathrm{x}}^3+12{\mathrm{x}}^2+\left|1+2\mathrm{x}\right|+\left|4\mathrm{x}\right|\mathrm{khi}-\frac{1}{2}\le \mathrm{x}\le 0.$

Giải các phương trình sau:

a) $\left|4-5\mathrm{x}\right|=\left|5-6\mathrm{x}\right|;$           b) $\left|3\mathrm{x}+2\right|-\left|7\mathrm{x}+1\right|=0;$ 

c) $\left|{\mathrm{x}}^2-2\mathrm{x}-3\right|+\left|\mathrm{x}+1\right|=0;$  d) $\frac{1}{4}\left|\mathrm{x}-5\right|=\left|3\mathrm{x}+1\right|$

Giải các phương trình sau:

a) $\left|\mathrm{x}-6\right|=-5\mathrm{x}+9;$            b) $\left|\mathrm{x}+1\right|={\mathrm{x}}^2+\mathrm{x};$ 

c) $\left|{\mathrm{x}}^2-2\mathrm{x}\right|+4=2\mathrm{x};$            d) $\left|\frac{{\mathrm{x}}^2-\mathrm{x}-6}{\mathrm{x}-1}\right|=\mathrm{x}-2.$

Giải phương trình sau bằng cách đặt ẩn phụ

a) $\left|{\mathrm{x}}^2-5\mathrm{x}+5\right|=-2{\mathrm{x}}^2+10\mathrm{x}-11.$

b) $3\left|{\mathrm{x}}^2+3\mathrm{x}\right|=\left(\mathrm{x}+5\right)\left(2-\mathrm{x}\right)+6.$

Rút gọn các biểu thức sau:

a) $\mathrm{A}=\left|\mathrm{x}-9\right|+7-\left|\mathrm{x}\right|$ khi $\mathrm{x}\ge 9$ 

b) $\mathrm{B}={\left|-3\mathrm{x}\right|}^2-8{\mathrm{x}}^2+\mathrm{x}-2$ khi $\text{x≥0}$

c) $\mathrm{C}=\left(\mathrm{x}+\frac{1}{2}\right)\left({\mathrm{x}}^2-\mathrm{x}+\left|\frac{1}{2}\mathrm{x}+\frac{1}{4}\right|\right)$ khi $\mathrm{x}>1$.

Giải các phương trình sau:

a) $\left|9-\mathrm{x}\right|=2\mathrm{x};$                          b) $\left|\mathrm{x}-15\right|+1=3\mathrm{x};$    

c) $\left|4{\mathrm{x}}^2-1\right|+3\mathrm{x}\left|2\mathrm{x}-1\right|=0;$      d) $\left|5-4\mathrm{x}\right|=4-5\mathrm{x}.$

Giải các phương trình sau:

a) $\left|\mathrm{x}+\frac{1}{3}\right|-5=1;$                       b) $\left|10\mathrm{x}-3\right|+\frac{1}{4}=5\%$ 

c) $3-\left|4\mathrm{x}-3\right|=-5+\left|4\mathrm{x}-3\right|$      d) $\frac{3\left|\mathrm{x}-11\right|}{2}-\frac{7}{3}=\frac{1}{3}\left|\mathrm{x}-11\right|.$

Giải các phương trình sau:

a) $2\left|5\mathrm{x}\right|-3=4;$                     b) $\frac{7}{2}-3\left|5-2\mathrm{x}\right|=\frac{9}{2}$ 

c) $\left|3\mathrm{x}-1\right|+4=6-\left|3\mathrm{x}-1\right|;$   d) $\frac{\left|3\mathrm{x}+4\right|}{2}-1=\frac{1}{3}$