解答 - 绝对值方程

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

从两边减去 $$$$:

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

组合分数:

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

合并分子:

$$-x+\frac{0}{2}=\left(\frac{1}{5}\right)-\frac{1}{2}$$

分子为零则整体为零:

$$-x+0=\left(\frac{1}{5}\right)-\frac{1}{2}$$

简化运算:

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

找出最小公分母:

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

乘以分母:

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

乘以分子:

$$-x=\frac{2}{10}+\frac{-5}{10}$$

组合分数:

$$-x=\frac{\left(2-5\right)}{10}$$

合并分子:

$$-x=\frac{-3}{10}$$

将 $$$$ 乘以两边:

$$-x·-1=\left(\frac{-3}{10}\right)·-1$$

删除乘以负一项:

$$x=\left(\frac{-3}{10}\right)·-1$$

删除乘以负一项:

$$x=\frac{3}{10}$$

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

交换边:

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

将 $$$$ 加到等式的两边:

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

组合分数:

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

合并分子:

$$x+\frac{0}{2}=\left(\frac{1}{5}\right)+\frac{1}{2}$$

分子为零则整体为零:

$$x+0=\left(\frac{1}{5}\right)+\frac{1}{2}$$

简化运算:

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

找出最小公分母:

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

乘以分母:

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

乘以分子:

$$x=\frac{2}{10}+\frac{5}{10}$$

组合分数:

$$x=\frac{\left(2+5\right)}{10}$$

合并分子:

$$x=\frac{7}{10}$$