解答 - 绝对值方程

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

收集同类项:

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

简化运算:

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

收集同类项:

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

简化运算:

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

陈述是错误的:

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

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

将 $$$$ 加到等式的两边:

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

收集同类项:

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

简化运算:

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

收集同类项:

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

简化运算:

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

将 $$$$ 加到等式的两边:

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

组合分数:

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

合并分子:

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

分子为零则整体为零:

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

简化运算:

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

找出最小公分母:

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

乘以分母:

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

乘以分子:

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

组合分数:

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

合并分子:

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

两边都除以 :

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

简化分数:

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

简化运算:

$$y=\frac{7}{\left(6·2\right)}$$

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