解答 - 绝对值方程

$$\left(\frac{3}{5}y\right)-\frac{3}{4}·y=\left(\frac{3}{4}y-7\right)-\frac{3}{4}y$$

将系数整合在一起:

$$\left(\frac{3}{5}+\frac{-3}{4}\right)y=\left(\frac{3}{4}·y-7\right)-\frac{3}{4}y$$

找出最小公分母:

$$\left(\frac{\left(3·4\right)}{\left(5·4\right)}+\frac{\left(-3·5\right)}{\left(4·5\right)}\right)y=\left(\frac{3}{4}·y-7\right)-\frac{3}{4}y$$

乘以分母:

$$\left(\frac{\left(3·4\right)}{20}+\frac{\left(-3·5\right)}{20}\right)y=\left(\frac{3}{4}·y-7\right)-\frac{3}{4}y$$

乘以分子:

$$\left(\frac{12}{20}+\frac{-15}{20}\right)y=\left(\frac{3}{4}·y-7\right)-\frac{3}{4}y$$

组合分数:

$$\frac{\left(12-15\right)}{20}·y=\left(\frac{3}{4}·y-7\right)-\frac{3}{4}y$$

合并分子:

$$\frac{-3}{20}·y=\left(\frac{3}{4}·y-7\right)-\frac{3}{4}y$$

收集同类项:

$$\frac{-3}{20}·y=\left(\frac{3}{4}·y+\frac{-3}{4}y\right)-7$$

组合分数:

$$\frac{-3}{20}·y=\frac{\left(3-3\right)}{4}y-7$$

合并分子:

$$\frac{-3}{20}·y=\frac{0}{4}y-7$$

分子为零则整体为零:

$$\frac{-3}{20}y=0y-7$$

简化运算:

$$\frac{-3}{20}y=-7$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{-3}{20}y\right)·\frac{20}{-3}=-7·\frac{20}{-3}$$

将负号从分母移至分子:

$$\frac{-3}{20}y·\frac{-20}{3}=-7·\frac{20}{-3}$$

收集同类项:

$$\left(\frac{-3}{20}·\frac{-20}{3}\right)y=-7·\frac{20}{-3}$$

系数之间相乘:

$$\frac{\left(-3·-20\right)}{\left(20·3\right)}y=-7·\frac{20}{-3}$$

简化运算:

$$1y=-7·\frac{20}{-3}$$

$$y=-7·\frac{20}{-3}$$

将负号从分母移至分子:

$$y=-7·\frac{-20}{3}$$

乘法分数:

$$y=\frac{\left(-7·-20\right)}{3}$$

简化运算:

$$y=\frac{140}{3}$$

$$\frac{3}{5}·y=\frac{-3}{4}y+7$$

将 $$$$ 加到等式的两边:

$$\left(\frac{3}{5}y\right)+\frac{3}{4}·y=\left(\frac{-3}{4}y+7\right)+\frac{3}{4}y$$

将系数整合在一起:

$$\left(\frac{3}{5}+\frac{3}{4}\right)y=\left(\frac{-3}{4}·y+7\right)+\frac{3}{4}y$$

找出最小公分母:

$$\left(\frac{\left(3·4\right)}{\left(5·4\right)}+\frac{\left(3·5\right)}{\left(4·5\right)}\right)y=\left(\frac{-3}{4}·y+7\right)+\frac{3}{4}y$$

乘以分母:

$$\left(\frac{\left(3·4\right)}{20}+\frac{\left(3·5\right)}{20}\right)y=\left(\frac{-3}{4}·y+7\right)+\frac{3}{4}y$$

乘以分子:

$$\left(\frac{12}{20}+\frac{15}{20}\right)y=\left(\frac{-3}{4}·y+7\right)+\frac{3}{4}y$$

组合分数:

$$\frac{\left(12+15\right)}{20}·y=\left(\frac{-3}{4}·y+7\right)+\frac{3}{4}y$$

合并分子:

$$\frac{27}{20}·y=\left(\frac{-3}{4}·y+7\right)+\frac{3}{4}y$$

收集同类项:

$$\frac{27}{20}·y=\left(\frac{-3}{4}·y+\frac{3}{4}y\right)+7$$

组合分数:

$$\frac{27}{20}·y=\frac{\left(-3+3\right)}{4}y+7$$

合并分子:

$$\frac{27}{20}·y=\frac{0}{4}y+7$$

分子为零则整体为零:

$$\frac{27}{20}y=0y+7$$

简化运算:

$$\frac{27}{20}y=7$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{27}{20}y\right)·\frac{20}{27}=7·\frac{20}{27}$$

收集同类项:

$$\left(\frac{27}{20}·\frac{20}{27}\right)y=7·\frac{20}{27}$$

系数之间相乘:

$$\frac{\left(27·20\right)}{\left(20·27\right)}y=7·\frac{20}{27}$$

简化分数:

$$y=7·\frac{20}{27}$$

乘法分数:

$$y=\frac{\left(7·20\right)}{27}$$

简化运算:

$$y=\frac{140}{27}$$