解答 - 绝对值方程

$$\left(r+\frac{3}{4}\right)-r=\left(r+\frac{-7}{8}\right)-r$$

收集同类项:

$$\left(r-r\right)+\frac{3}{4}=\left(r+\frac{-7}{8}\right)-r$$

简化运算:

$$\frac{3}{4}=\left(r+\frac{-7}{8}\right)-r$$

收集同类项:

$$\frac{3}{4}=\left(r-r\right)+\frac{-7}{8}$$

简化运算:

$$\frac{3}{4}=\frac{-7}{8}$$

陈述是错误的:

$$\frac{3}{4}=\frac{-7}{8}$$

$$\left(r+\frac{3}{4}\right)=-r+\frac{7}{8}$$

将 $$$$ 加到等式的两边:

$$\left(r+\frac{3}{4}\right)+r=\left(-r+\frac{7}{8}\right)+r$$

收集同类项:

$$\left(r+r\right)+\frac{3}{4}=\left(-r+\frac{7}{8}\right)+r$$

简化运算:

$$2r+\frac{3}{4}=\left(-r+\frac{7}{8}\right)+r$$

收集同类项:

$$2r+\frac{3}{4}=\left(-r+r\right)+\frac{7}{8}$$

简化运算:

$$2r+\frac{3}{4}=\frac{7}{8}$$

从两边减去 $$$$:

$$\left(2r+\frac{3}{4}\right)-\frac{3}{4}=\left(\frac{7}{8}\right)-\frac{3}{4}$$

组合分数:

$$2r+\frac{\left(3-3\right)}{4}=\left(\frac{7}{8}\right)-\frac{3}{4}$$

合并分子:

$$2r+\frac{0}{4}=\left(\frac{7}{8}\right)-\frac{3}{4}$$

分子为零则整体为零:

$$2r+0=\left(\frac{7}{8}\right)-\frac{3}{4}$$

简化运算:

$$2r=\left(\frac{7}{8}\right)-\frac{3}{4}$$

找出最小公分母:

$$2r=\frac{7}{8}+\frac{\left(-3·2\right)}{\left(4·2\right)}$$

乘以分母:

$$2r=\frac{7}{8}+\frac{\left(-3·2\right)}{8}$$

乘以分子:

$$2r=\frac{7}{8}+\frac{-6}{8}$$

组合分数:

$$2r=\frac{\left(7-6\right)}{8}$$

合并分子:

$$2r=\frac{1}{8}$$

两边都除以 :

$$\frac{\left(2r\right)}{2}=\frac{\left(\frac{1}{8}\right)}{2}$$

简化分数:

$$r=\frac{\left(\frac{1}{8}\right)}{2}$$

简化运算:

$$r=\frac{1}{\left(8·2\right)}$$

$$r=\frac{1}{16}$$