解答 - 绝对值方程

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

收集同类项:

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

将系数整合在一起:

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

将整数转换为分数:

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

组合分数:

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

合并分子:

$$\frac{6}{5}x+1=\left(-x+\frac{1}{2}\right)+x$$

收集同类项:

$$\frac{6}{5}x+1=\left(-x+x\right)+\frac{1}{2}$$

简化运算:

$$\frac{6}{5}x+1=\frac{1}{2}$$

从两边减去 $$$$:

$$\left(\frac{6}{5}x+1\right)-1=\left(\frac{1}{2}\right)-1$$

简化运算:

$$\frac{6}{5}x=\left(\frac{1}{2}\right)-1$$

将整数转换为分数:

$$\frac{6}{5}x=\frac{1}{2}+\frac{-2}{2}$$

组合分数:

$$\frac{6}{5}x=\frac{\left(1-2\right)}{2}$$

合并分子:

$$\frac{6}{5}x=\frac{-1}{2}$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{6}{5}x\right)·\frac{5}{6}=\left(\frac{-1}{2}\right)·\frac{5}{6}$$

收集同类项:

$$\left(\frac{6}{5}·\frac{5}{6}\right)x=\left(\frac{-1}{2}\right)·\frac{5}{6}$$

系数之间相乘:

$$\frac{\left(6·5\right)}{\left(5·6\right)}x=\left(\frac{-1}{2}\right)·\frac{5}{6}$$

简化分数:

$$x=\left(\frac{-1}{2}\right)·\frac{5}{6}$$

乘法分数:

$$x=\frac{\left(-1·5\right)}{\left(2·6\right)}$$

简化运算:

$$x=\frac{-5}{\left(2·6\right)}$$

$$x=\frac{-5}{12}$$

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

从两边减去 $$$$:

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

收集同类项:

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

将系数整合在一起:

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

将整数转换为分数:

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

组合分数:

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

合并分子:

$$\frac{-4}{5}x+1=\left(x+\frac{-1}{2}\right)-x$$

收集同类项:

$$\frac{-4}{5}x+1=\left(x-x\right)+\frac{-1}{2}$$

简化运算:

$$\frac{-4}{5}x+1=\frac{-1}{2}$$

从两边减去 $$$$:

$$\left(\frac{-4}{5}x+1\right)-1=\left(\frac{-1}{2}\right)-1$$

简化运算:

$$\frac{-4}{5}x=\left(\frac{-1}{2}\right)-1$$

将整数转换为分数:

$$\frac{-4}{5}x=\frac{-1}{2}+\frac{-2}{2}$$

组合分数:

$$\frac{-4}{5}x=\frac{\left(-1-2\right)}{2}$$

合并分子:

$$\frac{-4}{5}x=\frac{-3}{2}$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{-4}{5}x\right)·\frac{5}{-4}=\left(\frac{-3}{2}\right)·\frac{5}{-4}$$

将负号从分母移至分子:

$$\frac{-4}{5}x·\frac{-5}{4}=\left(\frac{-3}{2}\right)·\frac{5}{-4}$$

收集同类项:

$$\left(\frac{-4}{5}·\frac{-5}{4}\right)x=\left(\frac{-3}{2}\right)·\frac{5}{-4}$$

系数之间相乘:

$$\frac{\left(-4·-5\right)}{\left(5·4\right)}x=\left(\frac{-3}{2}\right)·\frac{5}{-4}$$

简化运算:

$$1x=\left(\frac{-3}{2}\right)·\frac{5}{-4}$$

$$x=\left(\frac{-3}{2}\right)·\frac{5}{-4}$$

将负号从分母移至分子:

$$x=\frac{-3}{2}·\frac{-5}{4}$$

乘法分数:

$$x=\frac{\left(-3·-5\right)}{\left(2·4\right)}$$

简化运算:

$$x=\frac{15}{\left(2·4\right)}$$

$$x=\frac{15}{8}$$