解答 - 绝对值方程

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

收集同类项:

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

简化运算:

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

收集同类项:

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

简化运算:

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

将 $$$$ 加到等式的两边:

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

组合分数:

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

合并分子:

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

分子为零则整体为零:

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

简化运算:

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

找出最小公分母:

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

乘以分母:

$$2x=\frac{\left(1·3\right)}{6}+\frac{\left(1·2\right)}{6}$$

乘以分子:

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

组合分数:

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

合并分子:

$$2x=\frac{5}{6}$$

两边都除以 :

$$\frac{\left(2x\right)}{2}=\frac{\left(\frac{5}{6}\right)}{2}$$

简化分数:

$$x=\frac{\left(\frac{5}{6}\right)}{2}$$

简化运算:

$$x=\frac{5}{\left(6·2\right)}$$

$$x=\frac{5}{12}$$

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

将 $$$$ 加到等式的两边:

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

收集同类项:

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

简化运算:

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

收集同类项:

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

简化运算:

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

将 $$$$ 加到等式的两边:

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

组合分数:

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

合并分子:

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

分子为零则整体为零:

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

简化运算:

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

找出最小公分母:

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

乘以分母:

$$4x=\frac{\left(-1·3\right)}{6}+\frac{\left(1·2\right)}{6}$$

乘以分子:

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

组合分数:

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

合并分子:

$$4x=\frac{-1}{6}$$

两边都除以 :

$$\frac{\left(4x\right)}{4}=\frac{\left(\frac{-1}{6}\right)}{4}$$

简化分数:

$$x=\frac{\left(\frac{-1}{6}\right)}{4}$$

简化运算:

$$x=\frac{-1}{\left(6·4\right)}$$

$$x=\frac{-1}{24}$$