解答 - 绝对值方程

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

收集同类项:

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

将系数整合在一起:

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

找出最小公分母:

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

乘以分母:

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

乘以分子:

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

组合分数:

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

合并分子:

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

收集同类项:

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

组合分数:

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

合并分子:

$$\frac{-1}{4}·x+2=\frac{0}{4}x-2$$

分子为零则整体为零:

$$\frac{-1}{4}x+2=0x-2$$

简化运算:

$$\frac{-1}{4}x+2=-2$$

从两边减去 $$$$:

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

简化运算:

$$\frac{-1}{4}x=-2-2$$

简化运算:

$$\frac{-1}{4}x=-4$$

两边都乘以倒数分数 $$$$:

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

收集同类项:

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

系数之间相乘:

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

简化运算:

$$1x=-4·\frac{4}{-1}$$

$$x=-4·\frac{4}{-1}$$

简化运算:

$$x=16$$

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

将 $$$$ 加到等式的两边:

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

收集同类项:

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

将系数整合在一起:

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

找出最小公分母:

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

乘以分母:

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

乘以分子:

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

组合分数:

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

合并分子:

$$\frac{5}{4}·x+2=\left(\frac{-3}{4}·x+2\right)+\frac{3}{4}x$$

收集同类项:

$$\frac{5}{4}·x+2=\left(\frac{-3}{4}·x+\frac{3}{4}x\right)+2$$

组合分数:

$$\frac{5}{4}·x+2=\frac{\left(-3+3\right)}{4}x+2$$

合并分子:

$$\frac{5}{4}·x+2=\frac{0}{4}x+2$$

分子为零则整体为零:

$$\frac{5}{4}x+2=0x+2$$

简化运算:

$$\frac{5}{4}x+2=2$$

从两边减去 $$$$:

$$\left(\frac{5}{4}x+2\right)-2=2-2$$

简化运算:

$$\frac{5}{4}x=2-2$$

简化运算:

$$\frac{5}{4}x=0$$

两边都除以系数:

$$x=0$$