2|x+1|-0,5=0,5
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4028 x 0,5 + 4028 + 2014 : \(\dfrac{1}{2}\) x 1,5 + 4028 : 0,5
= 4028 x 0,5 + 4028 x 1 + 2014 x 2 x 1,5 + 4028 x 2
= 4028 x 0,5 + 4028 x 1 + 4028 x 1,5 + 4028 x 2
= 4028 x ( 0,5 + 1 + 1,5 + 2)
= 4028 x 5
= 20140
a: \(=\dfrac{5}{4}\cdot\dfrac{2}{5}\cdot\dfrac{17}{21}\cdot\dfrac{7}{34}=\dfrac{1}{2}\cdot\dfrac{1}{2}\cdot\dfrac{1}{3}=\dfrac{1}{12}\)
b: =>0,5^x(0,5+1)=1,5
=>0,5^x=1
=>x=0
c: =>x*0,05-0,25*x=-1,2
=>-0,3*x=-1,2
=>x=4
d: =>x-1=1 hoặc x-1=-1
=>x=0 hoặc x=2
e: =5+4=9
1)\(x+0,5+x+1,5+x+2,5=33\)
\(\Leftrightarrow3x=33-0,5-1,5-2,5=28,5\)
\(\Leftrightarrow x=9,5\)
2)\(\left(x+0,9\right)\left(1-0,4\right)=2412\)
\(\Leftrightarrow\left(x+0,9\right)\cdot0,6=2412\)
\(\Leftrightarrow x+0,9=4020\)
\(\Leftrightarrow x=1019,1\)
1) \(5-\left(1+\dfrac{1}{3}\right):\left(1-\dfrac{1}{3}\right)\)
\(=5-\dfrac{4}{3}:\dfrac{2}{3}\)
\(=5-\dfrac{4}{3}\cdot\dfrac{3}{2}\)
\(=5-\dfrac{4}{2}\)
\(=5-2\)
\(=3\)
b) \(\left(1+\dfrac{2}{3}-\dfrac{5}{4}\right)-\left(1-\dfrac{5}{4}\right)+2022-\dfrac{2}{3}\)
\(=1+\dfrac{2}{3}-\dfrac{5}{4}-1+\dfrac{5}{4}++2022-\dfrac{2}{3}\)
\(=\left(1-1\right)+\left(\dfrac{2}{3}-\dfrac{2}{3}\right)+\left(-\dfrac{5}{4}+\dfrac{5}{4}\right)+2022\)
\(=0+0+0+2022\)
\(=2022\)
2) \(0,7^2\cdot x=0,49^2\)
\(\Rightarrow x=\dfrac{0,49^2}{0,7^2}\)
\(\Rightarrow x=\left(\dfrac{0,49}{0,7}\right)^2\)
\(\Rightarrow x=\left(0,7\right)^2\)
\(\Rightarrow x=0,49\)
b) \(x:\left(-0,5\right)^3=\left(0,5\right)^2\)
\(\Rightarrow x=\left(0,5\right)^2\cdot\left(-0,5\right)^3\)
\(\Rightarrow x=\left(-0,5\right)^5\)
\(\Rightarrow x=-\dfrac{1}{32}\)
2:
a: =>x*0,49=0,49^2
=>x=0,49
b: =>x=(0,5)^2*(-1)*(0,5)^3=-(0,5)^5
\(A=\dfrac{\sqrt{4x^2-4x+1}}{4x-2}=\dfrac{\sqrt{\left(2x-1\right)^2}}{2\left(2x-1\right)}=\dfrac{\left|2x-1\right|}{2\left(2x-1\right)}\)
\(\Rightarrow\left|A\right|=\left|\dfrac{\left|2x-1\right|}{2\left(2x-1\right)}\right|=\dfrac{\left|2x-1\right|}{2\left|2x-1\right|}=\dfrac{1}{2}\)
Ta có: \(A=\dfrac{\sqrt{4x^2-4x+1}}{4x-2}\)
\(=\dfrac{\left|2x-1\right|}{2\left(2x-1\right)}\)
\(=\left[{}\begin{matrix}-\dfrac{\left(2x-1\right)}{2\left(2x-1\right)}=-\dfrac{1}{2}\left(x< \dfrac{1}{2}\right)\\\dfrac{2x-1}{2\left(2x-1\right)}=\dfrac{1}{2}\left(x\ge\dfrac{1}{2}\right)\end{matrix}\right.\)
\(\Leftrightarrow\left|A\right|=0.5\)
0,5 x [ 0,5 x ( x - 0,5 ) - 0,5 ] = 0,5
[ 0,5 x ( x - 0,5 ) - 0,5 ] = 0,5 : 0,5
[ 0,5 x ( x - 0,5 ) - 0,5 ] = 1
0,5 x ( x - 0,5 ) = 1 - 0,5
0,5 x ( x - 0,5 ) = 0,5
( x - 0,5 ) = 0,5 : 0,5
x - 0,5 = 1
x = 1 + 0,5
x = 1,5
a.Ta có:|2x-1|=2x-1\(\Leftrightarrow\)2x-1\(\ge\)0\(\Leftrightarrow\)x\(\ge\)\(\dfrac{1}{2}\)
|2x-1|=1-2x\(\Leftrightarrow\)2x-1<0\(\Leftrightarrow\)x<\(\dfrac{1}{2}\)
ĐK:\(x\ge\dfrac{1}{2}\)
\(2x-1=2x-1\)
\(\Leftrightarrow2x-1-2x+1=0\)
\(\Leftrightarrow0x=0\)
\(\Rightarrow\)Tập no của PT là S={\(\forall x\)|x\(\ge\dfrac{1}{2}\)}
b.|0,5-3x|=3x-0,5\(\Leftrightarrow\)x<2,5
=0,5-3x\(\Leftrightarrow x\ge2,5\)
ĐK:x<2,5
Gỉai
0,5-3x=3x-0,5
\(\Leftrightarrow\)0,5-3x-3x+0,5=0
\(\Leftrightarrow\)1-6x=0
\(\Leftrightarrow x=\dfrac{1}{6}\)(TMĐKXĐ)
\(\Rightarrow\)tập no của PT là S={\(\dfrac{1}{6}\)}
c.|5x+1-10x|=0,5\(\Leftrightarrow\)|1-5x|=0,5\(\Leftrightarrow x< \dfrac{1}{5}\)
\(\Leftrightarrow\)|1-5x|=-0,5\(\Leftrightarrow\)x\(\ge\dfrac{1}{5}\)
ĐK:\(x< \dfrac{1}{5}\)
Gỉai
1-5x=0,5
\(\Leftrightarrow5x=0,5\)
\(\Leftrightarrow x=0,1\)(loại)
\(\Rightarrow pt\) trên vô nghiệm
d.|x+2|-|x-7|=0
ĐK:x\(\ne\pm2\);x\(\ne\pm7\)
Gỉai
\(\left\{{}\begin{matrix}x+2-x+7=0\\x-2-x-7=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-9=0\\-2x-9=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-9=0\left(KTMĐKXĐ\right)\\x=-4,5\left(TMĐKXĐ\right)\end{matrix}\right.\)
\(\Rightarrow\)tập no của phương trình là S={-4,5}
x= -1/2 hoặc x=-3/2 nha