解答 - 绝对值方程

$$\left(\frac{1}{4}w+5\right)-w=\left(w+1\right)-w$$

收集同类项:

$$\left(\frac{1}{4}w-w\right)+5=\left(w+1\right)-w$$

将系数整合在一起:

$$\left(\frac{1}{4}-1\right)w+5=\left(w+1\right)-w$$

将整数转换为分数:

$$\left(\frac{1}{4}+\frac{-4}{4}\right)w+5=\left(w+1\right)-w$$

组合分数:

$$\frac{\left(1-4\right)}{4}w+5=\left(w+1\right)-w$$

合并分子:

$$\frac{-3}{4}w+5=\left(w+1\right)-w$$

收集同类项:

$$\frac{-3}{4}w+5=\left(w-w\right)+1$$

简化运算:

$$\frac{-3}{4}w+5=1$$

从两边减去 $$$$:

$$\left(\frac{-3}{4}w+5\right)-5=1-5$$

简化运算:

$$\frac{-3}{4}w=1-5$$

简化运算:

$$\frac{-3}{4}w=-4$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{-3}{4}w\right)·\frac{4}{-3}=-4·\frac{4}{-3}$$

将负号从分母移至分子:

$$\frac{-3}{4}w·\frac{-4}{3}=-4·\frac{4}{-3}$$

收集同类项:

$$\left(\frac{-3}{4}·\frac{-4}{3}\right)w=-4·\frac{4}{-3}$$

系数之间相乘:

$$\frac{\left(-3·-4\right)}{\left(4·3\right)}w=-4·\frac{4}{-3}$$

简化运算:

$$1w=-4·\frac{4}{-3}$$

$$w=-4·\frac{4}{-3}$$

将负号从分母移至分子:

$$w=-4·\frac{-4}{3}$$

乘法分数:

$$w=\frac{\left(-4·-4\right)}{3}$$

简化运算:

$$w=\frac{16}{3}$$

$$\left(\frac{1}{4}w+5\right)=-w-1$$

将 $$$$ 加到等式的两边:

$$\left(\frac{1}{4}w+5\right)+w=\left(-w-1\right)+w$$

收集同类项:

$$\left(\frac{1}{4}w+w\right)+5=\left(-w-1\right)+w$$

将系数整合在一起:

$$\left(\frac{1}{4}+1\right)w+5=\left(-w-1\right)+w$$

将整数转换为分数:

$$\left(\frac{1}{4}+\frac{4}{4}\right)w+5=\left(-w-1\right)+w$$

组合分数:

$$\frac{\left(1+4\right)}{4}w+5=\left(-w-1\right)+w$$

合并分子:

$$\frac{5}{4}w+5=\left(-w-1\right)+w$$

收集同类项:

$$\frac{5}{4}w+5=\left(-w+w\right)-1$$

简化运算:

$$\frac{5}{4}w+5=-1$$

从两边减去 $$$$:

$$\left(\frac{5}{4}w+5\right)-5=-1-5$$

简化运算:

$$\frac{5}{4}w=-1-5$$

简化运算:

$$\frac{5}{4}w=-6$$

两边都乘以倒数分数 $$$$:

$$\left(\frac{5}{4}w\right)·\frac{4}{5}=-6·\frac{4}{5}$$

收集同类项:

$$\left(\frac{5}{4}·\frac{4}{5}\right)w=-6·\frac{4}{5}$$

系数之间相乘:

$$\frac{\left(5·4\right)}{\left(4·5\right)}w=-6·\frac{4}{5}$$

简化分数:

$$w=-6·\frac{4}{5}$$

乘法分数:

$$w=\frac{\left(-6·4\right)}{5}$$

简化运算:

$$w=\frac{-24}{5}$$