解答 - 绝对值方程

$$\left(26x+\frac{-1}{27}\right)-26x=\left(26x+\frac{1}{27}\right)-26x$$

收集同类项:

$$\left(26x-26x\right)+\frac{-1}{27}=\left(26x+\frac{1}{27}\right)-26x$$

简化运算:

$$\frac{-1}{27}=\left(26x+\frac{1}{27}\right)-26x$$

收集同类项:

$$\frac{-1}{27}=\left(26x-26x\right)+\frac{1}{27}$$

简化运算:

$$\frac{-1}{27}=\frac{1}{27}$$

陈述是错误的:

$$\frac{-1}{27}=\frac{1}{27}$$

$$\left(26x+\frac{-1}{27}\right)=-26x+\frac{-1}{27}$$

将 $$$$ 加到等式的两边:

$$\left(26x+\frac{-1}{27}\right)+26x=\left(-26x+\frac{-1}{27}\right)+26x$$

收集同类项:

$$\left(26x+26x\right)+\frac{-1}{27}=\left(-26x+\frac{-1}{27}\right)+26x$$

简化运算:

$$52x+\frac{-1}{27}=\left(-26x+\frac{-1}{27}\right)+26x$$

收集同类项:

$$52x+\frac{-1}{27}=\left(-26x+26x\right)+\frac{-1}{27}$$

简化运算:

$$52x+\frac{-1}{27}=\frac{-1}{27}$$

将 $$$$ 加到等式的两边:

$$\left(52x+\frac{-1}{27}\right)+\frac{1}{27}=\left(\frac{-1}{27}\right)+\frac{1}{27}$$

组合分数:

$$52x+\frac{\left(-1+1\right)}{27}=\left(\frac{-1}{27}\right)+\frac{1}{27}$$

合并分子:

$$52x+\frac{0}{27}=\left(\frac{-1}{27}\right)+\frac{1}{27}$$

分子为零则整体为零:

$$52x+0=\left(\frac{-1}{27}\right)+\frac{1}{27}$$

简化运算:

$$52x=\left(\frac{-1}{27}\right)+\frac{1}{27}$$

组合分数:

$$52x=\frac{\left(-1+1\right)}{27}$$

合并分子:

$$52x=\frac{0}{27}$$

分子为零则整体为零:

$$52x=0$$

两边都除以系数:

$$x=0$$