Bài tập theo tuần Toán 8 - Tuần 21

$\begin{array}{l}7+2x=32-3x\iff 5x=25\iff x=5\\ \\ \\ \\ \\ \\ \\ \end{array}$

$\begin{array}{l}A=B\iff \left(x-3\right)\left(x+4\right)-2\left(3x-2\right)={\left(x-4\right)}^2\\ \iff x^2+x-12-6x+4=x^2-8x+16\\ \iff 3x=24\iff x=8\end{array}$

$\begin{array}{l}a\left(ax+b\right)=b^2\left(x-1\right)\iff a^{2}x+ab=b^{2}x-b^2\\ \iff \left(a^2-b^2\right)x=-b\left(b+a\right)\iff x=\frac{-b\left(b+a\right)}{\left(a^2-b^2\right)}=\frac{b}{b-a}\end{array}$

$\begin{array}{l}\mathrm{1,2}-\left(x-\mathrm{0,8}\right)=-2.\left(\mathrm{0,9}+x\right)\\ \iff \mathrm{1,2}-x+\mathrm{0,8}=-\mathrm{1,8}+2x\iff 3x=\mathrm{3,8}\iff x=\frac{19}{15}\\ \\ \end{array}$

$x-\frac{\frac{x}{2}-\frac{3+x}{4}}{2}=3-\frac{\left(1-\frac{6-x}{3}\right).\frac{1}{2}}{2}\iff \frac{2x-\frac{2x-3-x}{4}}{2}=\frac{6-\frac{3-6+x}{3}.\frac{1}{2}}{2}$

$\begin{array}{l}\frac{8x-x+3}{4}=\frac{18+3-x}{6}\\ \iff \left(7x+3\right).6=\left(21-x\right).4\iff 42x+18=84-4x\iff x=\frac{33}{23}\end{array}$

$\begin{array}{l}\frac{7x-2}{12}+\frac{2-x}{4}=\frac{3x+1}{3}\iff \frac{7x-2+6-6x}{12}=\frac{4\left(3x+1\right)}{12}\\ \iff 4x+4=12x+4\iff 8x=0\iff x=0\end{array}$

$\begin{array}{l}\frac{x}{3}+\frac{2x-6}{6}=2-\frac{x}{3}\iff \frac{2x+2x-6}{6}=\frac{12-2x}{6}\\ \iff 4x-6=12-2x\iff 6x=18\iff x=3\\ \\ \end{array}$

$\begin{array}{l}\frac{x+1}{65}+\frac{x+3}{63}=\frac{x+5}{61}+\frac{x+7}{59}\\ \iff \frac{x+1}{65}+1+\frac{x+3}{63}+1=\frac{x+5}{61}+1+\frac{x+7}{59}+1\iff \frac{x+66}{65}+\frac{x+66}{63}=\frac{x+66}{61}+\frac{x+66}{59}\\ \\ \iff \left(x+66\right)\left(\frac{1}{65}-\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\iff x+66=0\iff x=-66\\ \end{array}$

$$\begin{gathered} \frac{14x-3}{15}=\frac{x+1}{9}+\frac{37x-23}{45}\iff \frac{42x-9}{45}=\frac{5x+5+37x-23}{45} \\ \iff 42x-9=42x-18\iff 0x=9\left(VN\right)\Rightarrow S=\varnothing \end{gathered}$$

$\begin{array}{l}\mathrm{2,3}x-2\left(\mathrm{0,7}+2x\right)=\mathrm{3,6}-\mathrm{1,7}x\\ \iff \mathrm{2,3}x-\mathrm{1,4}-4x=\mathrm{3,6}-\mathrm{1,7}x\iff 0x=5\left(ktm\right)S=\varnothing \end{array}$

$$\begin{gathered} 3.\left(\mathrm{2,2}-\mathrm{0,3}x\right)=\mathrm{2,6}+\left(\mathrm{0,1}x-4\right)\iff \mathrm{6,6}-\mathrm{0,9}x=\mathrm{2,6}+\mathrm{0,1}x-4 \\ \iff x=8S=\left\{8\right\} \end{gathered}$$

$$\begin{gathered} \mathrm{3,6}-\mathrm{0,5}\left(2x+1\right)=x-\mathrm{0,25}\left(2-4x\right) \\ \iff \mathrm{3,6}-x-\mathrm{0,5}=x-\frac{1}{2}+x\iff x=\mathrm{3,6}S=\left\{\mathrm{3,6}\right\} \end{gathered}$$