解答 - 绝对值方程

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

收集同类项:

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

简化运算:

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

收集同类项:

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

简化运算:

$$\frac{3}{4}=\frac{1}{2}$$

陈述是错误的:

$$\frac{3}{4}=\frac{1}{2}$$

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

将 $$$$ 加到等式的两边:

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

收集同类项:

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

简化运算:

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

收集同类项:

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

简化运算:

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

从两边减去 $$$$:

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

组合分数:

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

合并分子:

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

分子为零则整体为零:

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

简化运算:

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

找出最小公分母:

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

乘以分母:

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

乘以分子:

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

组合分数:

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

合并分子:

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

两边都除以 :

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

简化分数:

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

简化运算:

$$x=\frac{-5}{\left(4·2\right)}$$

$$x=\frac{-5}{8}$$