解答 - 绝对值方程

$$\left(\frac{9}{4}x-2\right)-8x=\left(8x+\frac{-2}{3}\right)-8x$$

收集同类项:

$$\left(\frac{9}{4}x-8x\right)-2=\left(8x+\frac{-2}{3}\right)-8x$$

将系数整合在一起:

$$\left(\frac{9}{4}-8\right)x-2=\left(8x+\frac{-2}{3}\right)-8x$$

将整数转换为分数:

$$\left(\frac{9}{4}+\frac{-32}{4}\right)x-2=\left(8x+\frac{-2}{3}\right)-8x$$

组合分数:

$$\frac{\left(9-32\right)}{4}x-2=\left(8x+\frac{-2}{3}\right)-8x$$

合并分子:

$$\frac{-23}{4}x-2=\left(8x+\frac{-2}{3}\right)-8x$$

收集同类项:

$$\frac{-23}{4}x-2=\left(8x-8x\right)+\frac{-2}{3}$$

简化运算:

$$\frac{-23}{4}x-2=\frac{-2}{3}$$

将 $$$$ 加到等式的两边:

$$\left(\frac{-23}{4}x-2\right)+2=\left(\frac{-2}{3}\right)+2$$

简化运算:

$$\frac{-23}{4}x=\left(\frac{-2}{3}\right)+2$$

将整数转换为分数:

$$\frac{-23}{4}x=\frac{-2}{3}+\frac{6}{3}$$

组合分数:

$$\frac{-23}{4}x=\frac{\left(-2+6\right)}{3}$$

合并分子:

$$\frac{-23}{4}x=\frac{4}{3}$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{-23}{4}x\right)·\frac{4}{-23}=\left(\frac{4}{3}\right)·\frac{4}{-23}$$

将负号从分母移至分子:

$$\frac{-23}{4}x·\frac{-4}{23}=\left(\frac{4}{3}\right)·\frac{4}{-23}$$

收集同类项:

$$\left(\frac{-23}{4}·\frac{-4}{23}\right)x=\left(\frac{4}{3}\right)·\frac{4}{-23}$$

系数之间相乘:

$$\frac{\left(-23·-4\right)}{\left(4·23\right)}x=\left(\frac{4}{3}\right)·\frac{4}{-23}$$

简化运算:

$$1x=\left(\frac{4}{3}\right)·\frac{4}{-23}$$

$$x=\left(\frac{4}{3}\right)·\frac{4}{-23}$$

将负号从分母移至分子:

$$x=\frac{4}{3}·\frac{-4}{23}$$

乘法分数:

$$x=\frac{\left(4·-4\right)}{\left(3·23\right)}$$

简化运算:

$$x=\frac{-16}{\left(3·23\right)}$$

$$x=\frac{-16}{69}$$

$$\left(\frac{9}{4}x-2\right)=-8x+\frac{2}{3}$$

将 $$$$ 加到等式的两边:

$$\left(\frac{9}{4}x-2\right)+8x=\left(-8x+\frac{2}{3}\right)+8x$$

收集同类项:

$$\left(\frac{9}{4}x+8x\right)-2=\left(-8x+\frac{2}{3}\right)+8x$$

将系数整合在一起:

$$\left(\frac{9}{4}+8\right)x-2=\left(-8x+\frac{2}{3}\right)+8x$$

将整数转换为分数:

$$\left(\frac{9}{4}+\frac{32}{4}\right)x-2=\left(-8x+\frac{2}{3}\right)+8x$$

组合分数:

$$\frac{\left(9+32\right)}{4}x-2=\left(-8x+\frac{2}{3}\right)+8x$$

合并分子:

$$\frac{41}{4}x-2=\left(-8x+\frac{2}{3}\right)+8x$$

收集同类项:

$$\frac{41}{4}x-2=\left(-8x+8x\right)+\frac{2}{3}$$

简化运算:

$$\frac{41}{4}x-2=\frac{2}{3}$$

将 $$$$ 加到等式的两边:

$$\left(\frac{41}{4}x-2\right)+2=\left(\frac{2}{3}\right)+2$$

简化运算:

$$\frac{41}{4}x=\left(\frac{2}{3}\right)+2$$

将整数转换为分数:

$$\frac{41}{4}x=\frac{2}{3}+\frac{6}{3}$$

组合分数:

$$\frac{41}{4}x=\frac{\left(2+6\right)}{3}$$

合并分子:

$$\frac{41}{4}x=\frac{8}{3}$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{41}{4}x\right)·\frac{4}{41}=\left(\frac{8}{3}\right)·\frac{4}{41}$$

收集同类项:

$$\left(\frac{41}{4}·\frac{4}{41}\right)x=\left(\frac{8}{3}\right)·\frac{4}{41}$$

系数之间相乘:

$$\frac{\left(41·4\right)}{\left(4·41\right)}x=\left(\frac{8}{3}\right)·\frac{4}{41}$$

简化分数:

$$x=\left(\frac{8}{3}\right)·\frac{4}{41}$$

乘法分数:

$$x=\frac{\left(8·4\right)}{\left(3·41\right)}$$

简化运算:

$$x=\frac{32}{\left(3·41\right)}$$

$$x=\frac{32}{123}$$