解答 - 绝对值方程

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

收集同类项:

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

将系数整合在一起:

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

将整数转换为分数:

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

组合分数:

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

合并分子:

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

收集同类项:

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

简化运算:

$$\frac{-1}{3}x-3=\frac{-1}{2}$$

将 $$$$ 加到等式的两边:

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

简化运算:

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

将整数转换为分数:

$$\frac{-1}{3}x=\frac{-1}{2}+\frac{6}{2}$$

组合分数:

$$\frac{-1}{3}x=\frac{\left(-1+6\right)}{2}$$

合并分子:

$$\frac{-1}{3}x=\frac{5}{2}$$

两边都乘以倒数分数 $$$$:

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

收集同类项:

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

系数之间相乘:

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

简化运算:

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

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

乘法分数:

$$x=\frac{\left(5·-3\right)}{2}$$

简化运算:

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

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

将 $$$$ 加到等式的两边:

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

收集同类项:

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

将系数整合在一起:

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

将整数转换为分数:

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

组合分数:

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

合并分子:

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

收集同类项:

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

简化运算:

$$\frac{5}{3}x-3=\frac{1}{2}$$

将 $$$$ 加到等式的两边:

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

简化运算:

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

将整数转换为分数:

$$\frac{5}{3}x=\frac{1}{2}+\frac{6}{2}$$

组合分数:

$$\frac{5}{3}x=\frac{\left(1+6\right)}{2}$$

合并分子:

$$\frac{5}{3}x=\frac{7}{2}$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{5}{3}x\right)·\frac{3}{5}=\left(\frac{7}{2}\right)·\frac{3}{5}$$

收集同类项:

$$\left(\frac{5}{3}·\frac{3}{5}\right)x=\left(\frac{7}{2}\right)·\frac{3}{5}$$

系数之间相乘:

$$\frac{\left(5·3\right)}{\left(3·5\right)}x=\left(\frac{7}{2}\right)·\frac{3}{5}$$

简化分数:

$$x=\left(\frac{7}{2}\right)·\frac{3}{5}$$

乘法分数:

$$x=\frac{\left(7·3\right)}{\left(2·5\right)}$$

简化运算:

$$x=\frac{21}{\left(2·5\right)}$$

$$x=\frac{21}{10}$$