解答 - 绝对值方程

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

收集同类项:

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

简化运算:

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

收集同类项:

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

简化运算:

$$\frac{2}{5}=3$$

陈述是错误的:

$$\frac{2}{5}=3$$

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

从两边减去 $$$$:

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

收集同类项:

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

简化运算:

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

收集同类项:

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

简化运算:

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

从两边减去 $$$$:

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

组合分数:

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

合并分子:

$$-2x+\frac{0}{5}=-3-\frac{2}{5}$$

分子为零则整体为零:

$$-2x+0=-3-\frac{2}{5}$$

简化运算:

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

将整数转换为分数:

$$-2x=\frac{-15}{5}+\frac{-2}{5}$$

组合分数:

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

合并分子:

$$-2x=\frac{-17}{5}$$

两边都除以 :

$$\frac{\left(-2x\right)}{-2}=\frac{\left(\frac{-17}{5}\right)}{-2}$$

消除负号:

$$\frac{2x}{2}=\frac{\left(\frac{-17}{5}\right)}{-2}$$

简化分数:

$$x=\frac{\left(\frac{-17}{5}\right)}{-2}$$

简化运算:

$$x=\frac{-17}{\left(5·-2\right)}$$

$$x=\frac{17}{10}$$