解答 - 绝对值方程

$$\left(\frac{-11}{3}x+8\right)+x=\left(-x+7\right)+x$$

收集同类项:

$$\left(\frac{-11}{3}x+x\right)+8=\left(-x+7\right)+x$$

将系数整合在一起:

$$\left(\frac{-11}{3}+1\right)x+8=\left(-x+7\right)+x$$

将整数转换为分数:

$$\left(\frac{-11}{3}+\frac{3}{3}\right)x+8=\left(-x+7\right)+x$$

组合分数:

$$\frac{\left(-11+3\right)}{3}x+8=\left(-x+7\right)+x$$

合并分子:

$$\frac{-8}{3}x+8=\left(-x+7\right)+x$$

收集同类项:

$$\frac{-8}{3}x+8=\left(-x+x\right)+7$$

简化运算:

$$\frac{-8}{3}x+8=7$$

从两边减去 $$$$:

$$\left(\frac{-8}{3}x+8\right)-8=7-8$$

简化运算:

$$\frac{-8}{3}x=7-8$$

简化运算:

$$\frac{-8}{3}x=-1$$

两边都乘以倒数分数 $$$$:

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

将负号从分母移至分子:

$$\frac{-8}{3}x·\frac{-3}{8}=-1·\frac{3}{-8}$$

收集同类项:

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

系数之间相乘:

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

简化运算:

$$1x=-1·\frac{3}{-8}$$

$$x=-1·\frac{3}{-8}$$

消除负号:

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

$$\left(\frac{-11}{3}x+8\right)=x-7$$

从两边减去 $$$$:

$$\left(\frac{-11}{3}x+8\right)-x=\left(x-7\right)-x$$

收集同类项:

$$\left(\frac{-11}{3}x-x\right)+8=\left(x-7\right)-x$$

将系数整合在一起:

$$\left(\frac{-11}{3}-1\right)x+8=\left(x-7\right)-x$$

将整数转换为分数:

$$\left(\frac{-11}{3}+\frac{-3}{3}\right)x+8=\left(x-7\right)-x$$

组合分数:

$$\frac{\left(-11-3\right)}{3}x+8=\left(x-7\right)-x$$

合并分子:

$$\frac{-14}{3}x+8=\left(x-7\right)-x$$

收集同类项:

$$\frac{-14}{3}x+8=\left(x-x\right)-7$$

简化运算:

$$\frac{-14}{3}x+8=-7$$

从两边减去 $$$$:

$$\left(\frac{-14}{3}x+8\right)-8=-7-8$$

简化运算:

$$\frac{-14}{3}x=-7-8$$

简化运算:

$$\frac{-14}{3}x=-15$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{-14}{3}x\right)·\frac{3}{-14}=-15·\frac{3}{-14}$$

将负号从分母移至分子:

$$\frac{-14}{3}x·\frac{-3}{14}=-15·\frac{3}{-14}$$

收集同类项:

$$\left(\frac{-14}{3}·\frac{-3}{14}\right)x=-15·\frac{3}{-14}$$

系数之间相乘:

$$\frac{\left(-14·-3\right)}{\left(3·14\right)}x=-15·\frac{3}{-14}$$

简化运算:

$$1x=-15·\frac{3}{-14}$$

$$x=-15·\frac{3}{-14}$$

将负号从分母移至分子:

$$x=-15·\frac{-3}{14}$$

乘法分数:

$$x=\frac{\left(-15·-3\right)}{14}$$

简化运算:

$$x=\frac{45}{14}$$