1.Rút gọn biểu thức Q=3x-4-|2x-1| 2.Tìm x, biết 0,25-|1,5-x|=0 04/07/2021 Bởi Vivian 1.Rút gọn biểu thức Q=3x-4-|2x-1| 2.Tìm x, biết 0,25-|1,5-x|=0
`1,` `Q=3x-4-|2x-1|` Nếu `2x-1≥0⇒2x≥1⇒x≥1/2` Thì `Q=3x-4-(2x-1)` `=3x-4-2x+1` `=(3x-2x)+(1-4)` `=x-3` Nếu `2x-1<0⇒2x<1⇒x<1/2` Thì `Q=3x-4-[-(2x-1)]` `=3x-4+2x-1` `=(3x+2x)-(1+4)` `=5x-5` `2,` `0,25-|1,5-x|=0` `⇒|1,5-x|=0,25` `⇒1,5-x=±0,25` \(⇒\left[ \begin{array}{l}1,5-x=0,25\\1,5-x=-0,25\end{array} \right.\) \(⇒\left[ \begin{array}{l}x=1,25\\x=1,75\end{array} \right.\) Bình luận
1/ $|2x-1|=\begin{cases}2x-1\,\,nếu\,\,2x-1≥0\,\,hay\,\,x≥\dfrac{1}{2}\\1-2x\,\,nếu\,\,2x-1<0\,\,hay\,\,x<\dfrac{1}{2}\end{cases}$ Với $x≥\dfrac{1}{2}→Q=3x-4-2x+1=x-3$ Với $x<\dfrac{1}{2}→Q=3x-4-1+2x=5x-5$ Vậy $Q=x-3$ với $x≥\dfrac{1}{2}$, $Q=5x-5$ với $x<\dfrac{1}{2}$ 2/ $0,25-|1,5-x|=0\\↔|1,5-x|=0,25\\↔\left[\begin{array}{1}1,5-x=0,25\\1,5-x=-0,25\end{array}\right.\\↔\left[\begin{array}{1}x=1,25\\x=1,75\end{array}\right.$ Vậy x=1,25 hoặc x=1,75 Bình luận
`1,` `Q=3x-4-|2x-1|`
Nếu `2x-1≥0⇒2x≥1⇒x≥1/2`
Thì `Q=3x-4-(2x-1)`
`=3x-4-2x+1`
`=(3x-2x)+(1-4)`
`=x-3`
Nếu `2x-1<0⇒2x<1⇒x<1/2`
Thì `Q=3x-4-[-(2x-1)]`
`=3x-4+2x-1`
`=(3x+2x)-(1+4)`
`=5x-5`
`2,` `0,25-|1,5-x|=0`
`⇒|1,5-x|=0,25`
`⇒1,5-x=±0,25`
\(⇒\left[ \begin{array}{l}1,5-x=0,25\\1,5-x=-0,25\end{array} \right.\)
\(⇒\left[ \begin{array}{l}x=1,25\\x=1,75\end{array} \right.\)
1/ $|2x-1|=\begin{cases}2x-1\,\,nếu\,\,2x-1≥0\,\,hay\,\,x≥\dfrac{1}{2}\\1-2x\,\,nếu\,\,2x-1<0\,\,hay\,\,x<\dfrac{1}{2}\end{cases}$
Với $x≥\dfrac{1}{2}→Q=3x-4-2x+1=x-3$
Với $x<\dfrac{1}{2}→Q=3x-4-1+2x=5x-5$
Vậy $Q=x-3$ với $x≥\dfrac{1}{2}$, $Q=5x-5$ với $x<\dfrac{1}{2}$
2/ $0,25-|1,5-x|=0\\↔|1,5-x|=0,25\\↔\left[\begin{array}{1}1,5-x=0,25\\1,5-x=-0,25\end{array}\right.\\↔\left[\begin{array}{1}x=1,25\\x=1,75\end{array}\right.$
Vậy x=1,25 hoặc x=1,75