解答 - 绝对值方程

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

收集同类项:

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

简化运算:

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

收集同类项:

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

简化运算:

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

陈述是错误的:

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

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

将 $$$$ 加到等式的两边:

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

收集同类项:

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

简化运算:

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

收集同类项:

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

简化运算:

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

将 $$$$ 加到等式的两边:

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

组合分数:

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

合并分子:

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

分子为零则整体为零:

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

简化运算:

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

找出最小公分母:

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

乘以分母:

$$2f=\frac{\left(-1·2\right)}{12}+\frac{\left(3·3\right)}{12}$$

乘以分子:

$$2f=\frac{-2}{12}+\frac{9}{12}$$

组合分数:

$$2f=\frac{\left(-2+9\right)}{12}$$

合并分子:

$$2f=\frac{7}{12}$$

两边都除以 :

$$\frac{\left(2f\right)}{2}=\frac{\left(\frac{7}{12}\right)}{2}$$

简化分数:

$$f=\frac{\left(\frac{7}{12}\right)}{2}$$

简化运算:

$$f=\frac{7}{\left(12·2\right)}$$

$$f=\frac{7}{24}$$