解答 - 绝对值方程

$$\left(\frac{7}{5}k\right)-\frac{1}{2}·k=\left(\frac{1}{2}k-2\right)-\frac{1}{2}k$$

将系数整合在一起:

$$\left(\frac{7}{5}+\frac{-1}{2}\right)k=\left(\frac{1}{2}·k-2\right)-\frac{1}{2}k$$

找出最小公分母:

$$\left(\frac{\left(7·2\right)}{\left(5·2\right)}+\frac{\left(-1·5\right)}{\left(2·5\right)}\right)k=\left(\frac{1}{2}·k-2\right)-\frac{1}{2}k$$

乘以分母:

$$\left(\frac{\left(7·2\right)}{10}+\frac{\left(-1·5\right)}{10}\right)k=\left(\frac{1}{2}·k-2\right)-\frac{1}{2}k$$

乘以分子:

$$\left(\frac{14}{10}+\frac{-5}{10}\right)k=\left(\frac{1}{2}·k-2\right)-\frac{1}{2}k$$

组合分数:

$$\frac{\left(14-5\right)}{10}·k=\left(\frac{1}{2}·k-2\right)-\frac{1}{2}k$$

合并分子:

$$\frac{9}{10}·k=\left(\frac{1}{2}·k-2\right)-\frac{1}{2}k$$

收集同类项:

$$\frac{9}{10}·k=\left(\frac{1}{2}·k+\frac{-1}{2}k\right)-2$$

组合分数:

$$\frac{9}{10}·k=\frac{\left(1-1\right)}{2}k-2$$

合并分子:

$$\frac{9}{10}·k=\frac{0}{2}k-2$$

分子为零则整体为零:

$$\frac{9}{10}k=0k-2$$

简化运算:

$$\frac{9}{10}k=-2$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{9}{10}k\right)·\frac{10}{9}=-2·\frac{10}{9}$$

收集同类项:

$$\left(\frac{9}{10}·\frac{10}{9}\right)k=-2·\frac{10}{9}$$

系数之间相乘:

$$\frac{\left(9·10\right)}{\left(10·9\right)}k=-2·\frac{10}{9}$$

简化分数:

$$k=-2·\frac{10}{9}$$

乘法分数:

$$k=\frac{\left(-2·10\right)}{9}$$

简化运算:

$$k=\frac{-20}{9}$$

$$\frac{7}{5}·k=\frac{-1}{2}k+2$$

将 $$$$ 加到等式的两边:

$$\left(\frac{7}{5}k\right)+\frac{1}{2}·k=\left(\frac{-1}{2}k+2\right)+\frac{1}{2}k$$

将系数整合在一起:

$$\left(\frac{7}{5}+\frac{1}{2}\right)k=\left(\frac{-1}{2}·k+2\right)+\frac{1}{2}k$$

找出最小公分母:

$$\left(\frac{\left(7·2\right)}{\left(5·2\right)}+\frac{\left(1·5\right)}{\left(2·5\right)}\right)k=\left(\frac{-1}{2}·k+2\right)+\frac{1}{2}k$$

乘以分母:

$$\left(\frac{\left(7·2\right)}{10}+\frac{\left(1·5\right)}{10}\right)k=\left(\frac{-1}{2}·k+2\right)+\frac{1}{2}k$$

乘以分子:

$$\left(\frac{14}{10}+\frac{5}{10}\right)k=\left(\frac{-1}{2}·k+2\right)+\frac{1}{2}k$$

组合分数:

$$\frac{\left(14+5\right)}{10}·k=\left(\frac{-1}{2}·k+2\right)+\frac{1}{2}k$$

合并分子:

$$\frac{19}{10}·k=\left(\frac{-1}{2}·k+2\right)+\frac{1}{2}k$$

收集同类项:

$$\frac{19}{10}·k=\left(\frac{-1}{2}·k+\frac{1}{2}k\right)+2$$

组合分数:

$$\frac{19}{10}·k=\frac{\left(-1+1\right)}{2}k+2$$

合并分子:

$$\frac{19}{10}·k=\frac{0}{2}k+2$$

分子为零则整体为零:

$$\frac{19}{10}k=0k+2$$

简化运算:

$$\frac{19}{10}k=2$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{19}{10}k\right)·\frac{10}{19}=2·\frac{10}{19}$$

收集同类项:

$$\left(\frac{19}{10}·\frac{10}{19}\right)k=2·\frac{10}{19}$$

系数之间相乘:

$$\frac{\left(19·10\right)}{\left(10·19\right)}k=2·\frac{10}{19}$$

简化分数:

$$k=2·\frac{10}{19}$$

乘法分数:

$$k=\frac{\left(2·10\right)}{19}$$

简化运算:

$$k=\frac{20}{19}$$