解答 - 绝对值方程

$$\left(\frac{1}{3}x\right)-\frac{2}{5}·x=\left(\frac{2}{5}x\right)-\frac{2}{5}x$$

将系数整合在一起:

$$\left(\frac{1}{3}+\frac{-2}{5}\right)x=\left(\frac{2}{5}·x\right)-\frac{2}{5}x$$

找出最小公分母:

$$\left(\frac{\left(1·5\right)}{\left(3·5\right)}+\frac{\left(-2·3\right)}{\left(5·3\right)}\right)x=\left(\frac{2}{5}·x\right)-\frac{2}{5}x$$

乘以分母:

$$\left(\frac{\left(1·5\right)}{15}+\frac{\left(-2·3\right)}{15}\right)x=\left(\frac{2}{5}·x\right)-\frac{2}{5}x$$

乘以分子:

$$\left(\frac{5}{15}+\frac{-6}{15}\right)x=\left(\frac{2}{5}·x\right)-\frac{2}{5}x$$

组合分数:

$$\frac{\left(5-6\right)}{15}·x=\left(\frac{2}{5}·x\right)-\frac{2}{5}x$$

合并分子:

$$\frac{-1}{15}·x=\left(\frac{2}{5}·x\right)-\frac{2}{5}x$$

组合分数:

$$\frac{-1}{15}·x=\frac{\left(2-2\right)}{5}x$$

合并分子:

$$\frac{-1}{15}·x=\frac{0}{5}x$$

分子为零则整体为零:

$$\frac{-1}{15}x=0x$$

简化运算:

$$\frac{-1}{15}x=0$$

两边都除以系数:

$$x=0$$

$$\left(\frac{1}{3}x\right)·\frac{3}{1}=\left(\frac{-2}{5}x\right)·\frac{3}{1}$$

收集同类项:

$$\left(\frac{1}{3}·3\right)x=\left(\frac{-2}{5}x\right)·\frac{3}{1}$$

系数之间相乘:

$$\frac{\left(1·3\right)}{3}·x=\left(\frac{-2}{5}x\right)·\frac{3}{1}$$

简化分数:

$$x=\left(\frac{-2}{5}x\right)·\frac{3}{1}$$

收集同类项:

$$x=\left(\frac{-2}{5}·3\right)x$$

系数之间相乘:

$$x=\frac{\left(-2·3\right)}{5}x$$

简化运算:

$$x=\frac{-6}{5}x$$

将 $$$$ 加到等式的两边:

$$x+\frac{6}{5}·x=\left(\frac{-6}{5}x\right)+\frac{6}{5}x$$

将系数整合在一起:

$$\left(1+\frac{6}{5}\right)x=\left(\frac{-6}{5}·x\right)+\frac{6}{5}x$$

将整数转换为分数:

$$\left(\frac{5}{5}+\frac{6}{5}\right)x=\left(\frac{-6}{5}·x\right)+\frac{6}{5}x$$

组合分数:

$$\frac{\left(5+6\right)}{5}·x=\left(\frac{-6}{5}·x\right)+\frac{6}{5}x$$

合并分子:

$$\frac{11}{5}·x=\left(\frac{-6}{5}·x\right)+\frac{6}{5}x$$

组合分数:

$$\frac{11}{5}·x=\frac{\left(-6+6\right)}{5}x$$

合并分子:

$$\frac{11}{5}·x=\frac{0}{5}x$$

分子为零则整体为零:

$$\frac{11}{5}x=0x$$

简化运算:

$$\frac{11}{5}x=0$$

两边都除以系数:

$$x=0$$