解答 - 绝对值方程

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

将系数整合在一起:

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

将整数转换为分数:

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

组合分数:

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

合并分子:

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

收集同类项:

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

简化运算:

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

两边都乘以倒数分数 $$$$:

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

将负号从分母移至分子:

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

收集同类项:

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

系数之间相乘:

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

简化运算:

$$1x=-3·\frac{5}{-3}$$

$$x=-3·\frac{5}{-3}$$

将负号从分母移至分子:

$$x=-3·\frac{-5}{3}$$

乘法分数:

$$x=\frac{\left(-3·-5\right)}{3}$$

简化运算:

$$x=5$$

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

将 $$$$ 加到等式的两边:

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

将系数整合在一起:

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

将整数转换为分数:

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

组合分数:

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

合并分子:

$$\frac{7}{5}x=\left(-x+3\right)+x$$

收集同类项:

$$\frac{7}{5}x=\left(-x+x\right)+3$$

简化运算:

$$\frac{7}{5}x=3$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{7}{5}x\right)·\frac{5}{7}=3·\frac{5}{7}$$

收集同类项:

$$\left(\frac{7}{5}·\frac{5}{7}\right)x=3·\frac{5}{7}$$

系数之间相乘:

$$\frac{\left(7·5\right)}{\left(5·7\right)}x=3·\frac{5}{7}$$

简化分数:

$$x=3·\frac{5}{7}$$

乘法分数:

$$x=\frac{\left(3·5\right)}{7}$$

简化运算:

$$x=\frac{15}{7}$$