解答 - 绝对值方程

$$\left(x-2\right)-\frac{1}{3}·x=\left(\frac{1}{3}x\right)-\frac{1}{3}x$$

收集同类项:

$$\left(x+\frac{-1}{3}·x\right)-2=\left(\frac{1}{3}·x\right)-\frac{1}{3}x$$

将系数整合在一起:

$$\left(1+\frac{-1}{3}\right)x-2=\left(\frac{1}{3}·x\right)-\frac{1}{3}x$$

将整数转换为分数:

$$\left(\frac{3}{3}+\frac{-1}{3}\right)x-2=\left(\frac{1}{3}·x\right)-\frac{1}{3}x$$

组合分数:

$$\frac{\left(3-1\right)}{3}·x-2=\left(\frac{1}{3}·x\right)-\frac{1}{3}x$$

合并分子:

$$\frac{2}{3}·x-2=\left(\frac{1}{3}·x\right)-\frac{1}{3}x$$

组合分数:

$$\frac{2}{3}·x-2=\frac{\left(1-1\right)}{3}x$$

合并分子:

$$\frac{2}{3}·x-2=\frac{0}{3}x$$

分子为零则整体为零:

$$\frac{2}{3}x-2=0x$$

简化运算:

$$\frac{2}{3}x-2=0$$

将 $$$$ 加到等式的两边:

$$\left(\frac{2}{3}x-2\right)+2=0+2$$

简化运算:

$$\frac{2}{3}x=0+2$$

简化运算:

$$\frac{2}{3}x=2$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{2}{3}x\right)·\frac{3}{2}=2·\frac{3}{2}$$

收集同类项:

$$\left(\frac{2}{3}·\frac{3}{2}\right)x=2·\frac{3}{2}$$

系数之间相乘:

$$\frac{\left(2·3\right)}{\left(3·2\right)}x=2·\frac{3}{2}$$

简化分数:

$$x=2·\frac{3}{2}$$

乘法分数:

$$x=\frac{\left(2·3\right)}{2}$$

简化运算:

$$x=3$$

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

简化运算:

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

将 $$$$ 加到等式的两边:

$$x+\frac{1}{3}·x=\left(\frac{-1}{3}x+2\right)+\frac{1}{3}x$$

将系数整合在一起:

$$\left(1+\frac{1}{3}\right)x=\left(\frac{-1}{3}·x+2\right)+\frac{1}{3}x$$

将整数转换为分数:

$$\left(\frac{3}{3}+\frac{1}{3}\right)x=\left(\frac{-1}{3}·x+2\right)+\frac{1}{3}x$$

组合分数:

$$\frac{\left(3+1\right)}{3}·x=\left(\frac{-1}{3}·x+2\right)+\frac{1}{3}x$$

合并分子:

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

收集同类项:

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

组合分数:

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

合并分子:

$$\frac{4}{3}·x=\frac{0}{3}x+2$$

分子为零则整体为零:

$$\frac{4}{3}x=0x+2$$

简化运算:

$$\frac{4}{3}x=2$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{4}{3}x\right)·\frac{3}{4}=2·\frac{3}{4}$$

收集同类项:

$$\left(\frac{4}{3}·\frac{3}{4}\right)x=2·\frac{3}{4}$$

系数之间相乘:

$$\frac{\left(4·3\right)}{\left(3·4\right)}x=2·\frac{3}{4}$$

简化分数:

$$x=2·\frac{3}{4}$$

乘法分数:

$$x=\frac{\left(2·3\right)}{4}$$

简化运算:

$$x=\frac{3}{2}$$