解答 - 绝对值方程

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

收集同类项:

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

将系数整合在一起:

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

找出最小公分母:

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

乘以分母:

$$\left(\frac{\left(3·3\right)}{15}+\frac{\left(-2·5\right)}{15}\right)y-4=\left(\frac{2}{3}·y\right)-\frac{2}{3}y$$

乘以分子:

$$\left(\frac{9}{15}+\frac{-10}{15}\right)y-4=\left(\frac{2}{3}·y\right)-\frac{2}{3}y$$

组合分数:

$$\frac{\left(9-10\right)}{15}·y-4=\left(\frac{2}{3}·y\right)-\frac{2}{3}y$$

合并分子:

$$\frac{-1}{15}·y-4=\left(\frac{2}{3}·y\right)-\frac{2}{3}y$$

组合分数:

$$\frac{-1}{15}·y-4=\frac{\left(2-2\right)}{3}y$$

合并分子:

$$\frac{-1}{15}·y-4=\frac{0}{3}y$$

分子为零则整体为零:

$$\frac{-1}{15}y-4=0y$$

简化运算:

$$\frac{-1}{15}y-4=0$$

将 $$$$ 加到等式的两边:

$$\left(\frac{-1}{15}y-4\right)+4=0+4$$

简化运算:

$$\frac{-1}{15}y=0+4$$

简化运算:

$$\frac{-1}{15}y=4$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{-1}{15}y\right)·\frac{15}{-1}=4·\frac{15}{-1}$$

收集同类项:

$$\left(\frac{-1}{15}·-15\right)y=4·\frac{15}{-1}$$

系数之间相乘:

$$\frac{\left(-1·-15\right)}{15}y=4·\frac{15}{-1}$$

简化运算:

$$1y=4·\frac{15}{-1}$$

$$y=4·\frac{15}{-1}$$

简化运算:

$$y=-60$$

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

简化运算:

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

将 $$$$ 加到等式的两边:

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

将系数整合在一起:

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

找出最小公分母:

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

乘以分母:

$$\left(\frac{\left(3·3\right)}{15}+\frac{\left(2·5\right)}{15}\right)y=\left(\frac{-2}{3}·y+4\right)+\frac{2}{3}y$$

乘以分子:

$$\left(\frac{9}{15}+\frac{10}{15}\right)y=\left(\frac{-2}{3}·y+4\right)+\frac{2}{3}y$$

组合分数:

$$\frac{\left(9+10\right)}{15}·y=\left(\frac{-2}{3}·y+4\right)+\frac{2}{3}y$$

合并分子:

$$\frac{19}{15}·y=\left(\frac{-2}{3}·y+4\right)+\frac{2}{3}y$$

收集同类项:

$$\frac{19}{15}·y=\left(\frac{-2}{3}·y+\frac{2}{3}y\right)+4$$

组合分数:

$$\frac{19}{15}·y=\frac{\left(-2+2\right)}{3}y+4$$

合并分子:

$$\frac{19}{15}·y=\frac{0}{3}y+4$$

分子为零则整体为零:

$$\frac{19}{15}y=0y+4$$

简化运算:

$$\frac{19}{15}y=4$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{19}{15}y\right)·\frac{15}{19}=4·\frac{15}{19}$$

收集同类项:

$$\left(\frac{19}{15}·\frac{15}{19}\right)y=4·\frac{15}{19}$$

系数之间相乘:

$$\frac{\left(19·15\right)}{\left(15·19\right)}y=4·\frac{15}{19}$$

简化分数:

$$y=4·\frac{15}{19}$$

乘法分数:

$$y=\frac{\left(4·15\right)}{19}$$

简化运算:

$$y=\frac{60}{19}$$