解答 - 绝对值方程

$$\left(x+\frac{-4}{3}\right)-x=\left(x+\frac{1}{6}\right)-x$$

收集同类项:

$$\left(x-x\right)+\frac{-4}{3}=\left(x+\frac{1}{6}\right)-x$$

简化运算:

$$\frac{-4}{3}=\left(x+\frac{1}{6}\right)-x$$

收集同类项:

$$\frac{-4}{3}=\left(x-x\right)+\frac{1}{6}$$

简化运算:

$$\frac{-4}{3}=\frac{1}{6}$$

陈述是错误的:

$$\frac{-4}{3}=\frac{1}{6}$$

$$\left(x+\frac{-4}{3}\right)=-x+\frac{-1}{6}$$

将 $$$$ 加到等式的两边:

$$\left(x+\frac{-4}{3}\right)+x=\left(-x+\frac{-1}{6}\right)+x$$

收集同类项:

$$\left(x+x\right)+\frac{-4}{3}=\left(-x+\frac{-1}{6}\right)+x$$

简化运算:

$$2x+\frac{-4}{3}=\left(-x+\frac{-1}{6}\right)+x$$

收集同类项:

$$2x+\frac{-4}{3}=\left(-x+x\right)+\frac{-1}{6}$$

简化运算:

$$2x+\frac{-4}{3}=\frac{-1}{6}$$

将 $$$$ 加到等式的两边:

$$\left(2x+\frac{-4}{3}\right)+\frac{4}{3}=\left(\frac{-1}{6}\right)+\frac{4}{3}$$

组合分数:

$$2x+\frac{\left(-4+4\right)}{3}=\left(\frac{-1}{6}\right)+\frac{4}{3}$$

合并分子:

$$2x+\frac{0}{3}=\left(\frac{-1}{6}\right)+\frac{4}{3}$$

分子为零则整体为零:

$$2x+0=\left(\frac{-1}{6}\right)+\frac{4}{3}$$

简化运算:

$$2x=\left(\frac{-1}{6}\right)+\frac{4}{3}$$

找出最小公分母:

$$2x=\frac{-1}{6}+\frac{\left(4·2\right)}{\left(3·2\right)}$$

乘以分母:

$$2x=\frac{-1}{6}+\frac{\left(4·2\right)}{6}$$

乘以分子:

$$2x=\frac{-1}{6}+\frac{8}{6}$$

组合分数:

$$2x=\frac{\left(-1+8\right)}{6}$$

合并分子:

$$2x=\frac{7}{6}$$

两边都除以 :

$$\frac{\left(2x\right)}{2}=\frac{\left(\frac{7}{6}\right)}{2}$$

简化分数:

$$x=\frac{\left(\frac{7}{6}\right)}{2}$$

简化运算:

$$x=\frac{7}{\left(6·2\right)}$$

$$x=\frac{7}{12}$$