解答 - 绝对值方程

$$\left(\frac{7}{8}x\right)-\frac{1}{2}·x=\left(\frac{1}{2}x\right)-\frac{1}{2}x$$

将系数整合在一起:

$$\left(\frac{7}{8}+\frac{-1}{2}\right)x=\left(\frac{1}{2}·x\right)-\frac{1}{2}x$$

找出最小公分母:

$$\left(\frac{7}{8}+\frac{\left(-1·4\right)}{\left(2·4\right)}\right)x=\left(\frac{1}{2}·x\right)-\frac{1}{2}x$$

乘以分母:

$$\left(\frac{7}{8}+\frac{\left(-1·4\right)}{8}\right)x=\left(\frac{1}{2}·x\right)-\frac{1}{2}x$$

乘以分子:

$$\left(\frac{7}{8}+\frac{-4}{8}\right)x=\left(\frac{1}{2}·x\right)-\frac{1}{2}x$$

组合分数:

$$\frac{\left(7-4\right)}{8}·x=\left(\frac{1}{2}·x\right)-\frac{1}{2}x$$

合并分子:

$$\frac{3}{8}·x=\left(\frac{1}{2}·x\right)-\frac{1}{2}x$$

组合分数:

$$\frac{3}{8}·x=\frac{\left(1-1\right)}{2}x$$

合并分子:

$$\frac{3}{8}·x=\frac{0}{2}x$$

分子为零则整体为零:

$$\frac{3}{8}x=0x$$

简化运算:

$$\frac{3}{8}x=0$$

两边都除以系数:

$$x=0$$

$$\left(\frac{7}{8}x\right)·\frac{8}{7}=\left(\frac{-1}{2}x\right)·\frac{8}{7}$$

收集同类项:

$$\left(\frac{7}{8}·\frac{8}{7}\right)x=\left(\frac{-1}{2}x\right)·\frac{8}{7}$$

系数之间相乘:

$$\frac{\left(7·8\right)}{\left(8·7\right)}·x=\left(\frac{-1}{2}x\right)·\frac{8}{7}$$

简化分数:

$$x=\left(\frac{-1}{2}x\right)·\frac{8}{7}$$

收集同类项:

$$x=\left(\frac{-1}{2}·\frac{8}{7}\right)x$$

系数之间相乘:

$$x=\frac{\left(-1·8\right)}{\left(2·7\right)}x$$

简化运算:

$$x=\frac{-4}{7}x$$

将 $$$$ 加到等式的两边:

$$x+\frac{4}{7}·x=\left(\frac{-4}{7}x\right)+\frac{4}{7}x$$

将系数整合在一起:

$$\left(1+\frac{4}{7}\right)x=\left(\frac{-4}{7}·x\right)+\frac{4}{7}x$$

将整数转换为分数:

$$\left(\frac{7}{7}+\frac{4}{7}\right)x=\left(\frac{-4}{7}·x\right)+\frac{4}{7}x$$

组合分数:

$$\frac{\left(7+4\right)}{7}·x=\left(\frac{-4}{7}·x\right)+\frac{4}{7}x$$

合并分子:

$$\frac{11}{7}·x=\left(\frac{-4}{7}·x\right)+\frac{4}{7}x$$

组合分数:

$$\frac{11}{7}·x=\frac{\left(-4+4\right)}{7}x$$

合并分子:

$$\frac{11}{7}·x=\frac{0}{7}x$$

分子为零则整体为零:

$$\frac{11}{7}x=0x$$

简化运算:

$$\frac{11}{7}x=0$$

两边都除以系数:

$$x=0$$