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a)
<=> 3x - 3 + x - 2 = 2x - 2 - x + 1
<=> 3x + x - 2x + x = -2 + 1 + 3 + 2
<=> 3x = 4
<=> x = 4/3
Các câu sau làm tương tự
\(\left(3x-3\right)+\left(x-2\right)=\left(2x-2\right)-\left(x-1\right)\)
<=> \(3x-3+x-2=2x-2-x+1\)
<=> \(4x-5=x-1\)
<=> \(3x=4\)
<=> \(x=\frac{4}{3}\)
Vậy....
a; -2\(x\) - 3.(\(x-17\)) = 34 - 2.( - \(x\) + 25)
- 2\(x\) - 3\(x\) + 51 = 34 + 2\(x\) - 50
2\(x\) + 2\(x\) + 3\(x\) = - 34 + 50 + 51
7\(x\) = 67
\(x\) = 67 : 7
\(x\) = \(\dfrac{67}{7}\)
Vậy \(x\) = \(\dfrac{67}{7}\)
b; 17\(x\) + 3.(- 16\(x\) - 37) = 2\(x\) + 43 - 4\(x\)
17\(x\) - 48\(x\) - 111 = 2\(x\) - 4\(x\) + 43
- 31\(x\) - 2\(x\) + 4\(x\) = 111 + 43
- \(x\) x (31 + 2 - 4) = 154
- \(x\) x (33 - 4) = 154
- \(x\) x 29 = 154
- \(x\) = 154 : (-29)
\(x\) = - \(\dfrac{154}{29}\)
Vậy \(x=-\dfrac{154}{29}\)
c) x.(1+2+3+4+...+100)=0
x.5050=0
x=0:5050=0
Vậy x=0
d) x.(1+2+3+4+5+...+100)=5050
x.5050=5050
x=1
Vậy x=1
e) x+1+x+2+x+3+x+4+...+x+100=5050
(x+x+x+x+...+x)+(1+2+3+4+...+100)=5050
100 số hạng x
x.100+5050=5050
x.100=0
x=0
Vậy x=0
a, 2x -(-17) = 15
2x + 17 = 15
2x = 15 - 17
2x =(-2)
x = (-2) : 2
x = (-1)
a ) \(-5\times\left(-x+7\right)-3\times\left(-x-5\right)=-4\times\left(12-x\right)+48\)
\(\Leftrightarrow5x-35+3x+15=-48+4x+48\)
\(\Leftrightarrow5x-3x+4x=35-15-48+48\)
\(\Leftrightarrow2x=20\)
\(\Leftrightarrow x=10\)
b ) \(-2\times\left(15-3x\right)-4\times\left(-7x+8\right)=-5-9\times\left(-2x+1\right)\)
\(\Leftrightarrow-30+6x-28x-32=-5+18x-9\)
\(\Leftrightarrow6x-28x-18x=30+32-5-9\)
\(\Leftrightarrow-40x=48\)
\(\Leftrightarrow x=-1.2\)
a) \(\left|4+2x\right|=-4x\)
th1: \(4+2x\ge0\Leftrightarrow2x\ge-4\Leftrightarrow x\ge\dfrac{-4}{2}=-2\)
\(\Rightarrow\left|4+2x\right|=-4x\Leftrightarrow4+2x=-4x\Leftrightarrow4=-4x-2x=-6x\)
\(\Leftrightarrow x=\dfrac{4}{-6}=\dfrac{-2}{3}\left(tmđk\right)\)
th2: \(4+2x< 0\Leftrightarrow2x< -4\Leftrightarrow x< \dfrac{-4}{2}=-2\)
\(\Rightarrow\left|4+2x\right|=-4x\Leftrightarrow-4-2x=-4x\Leftrightarrow-4=-4x+2x=-2x\)
\(\Leftrightarrow x=\dfrac{-4}{-2}=2\left(loại\right)\)
vậy \(x=\dfrac{-2}{3}\)
b) \(\left|3x-1\right|+2=x\)
th1: \(3x-1\ge0\Leftrightarrow3x\ge1\Leftrightarrow x\ge\dfrac{1}{3}\)
\(\Rightarrow\left|3x-1\right|+2=x\Leftrightarrow3x-1+2=x\Leftrightarrow3x-x=1-2\)
\(\Leftrightarrow2x=-1\Leftrightarrow x=\dfrac{-1}{2}\left(loại\right)\)
th2: \(3x-1< 0\Leftrightarrow3x< 1\Leftrightarrow x< \dfrac{1}{3}\)
\(\Rightarrow\left|3x-1\right|+2=x\Leftrightarrow1-3x+2=x\Leftrightarrow x+3x=1+2\)
\(\Leftrightarrow4x=3\Leftrightarrow x=\dfrac{3}{4}\left(loại\right)\)
vậy phương trình vô nghiệm
c) \(\left|x+15\right|+1=3x\)
th1: \(x+15\ge0\Leftrightarrow x\ge-15\)
\(\Rightarrow\left|x+15\right|+1=3x\Leftrightarrow x+15+1=3x\Leftrightarrow3x-x=15+1\)
\(\Leftrightarrow2x=16\Leftrightarrow x=\dfrac{16}{2}=8\left(tmđk\right)\)
th2: \(x+15< 0\Leftrightarrow x< -15\)
\(\Rightarrow\left|x+15\right|+1=3x\Leftrightarrow-x-15+1=3x\Leftrightarrow3x+x=-15+1\)
\(\Leftrightarrow4x=-14\Leftrightarrow x=\dfrac{-14}{4}=\dfrac{-7}{2}\left(loại\right)\)
vậy \(x=8\)
d) \(\left|2x-5\right|+x=2\)
th1: \(2x-5\ge0\Leftrightarrow2x\ge5\Leftrightarrow x\ge\dfrac{5}{2}\)
\(\Rightarrow\left|2x-5\right|+x=2\Leftrightarrow2x-5+x=2\Leftrightarrow2x+x=2+5\)
\(\Leftrightarrow3x=7\Leftrightarrow x=\dfrac{7}{3}\left(loại\right)\)
th2: \(2x-5< 0\Leftrightarrow2x< 5\Leftrightarrow x< \dfrac{5}{2}\)
\(\Rightarrow\left|2x-5\right|+x=2\Leftrightarrow5-2x+x=2\Leftrightarrow-2x+x=2-5\)
\(\Leftrightarrow-x=-3\Leftrightarrow x=3\left(loại\right)\)
vậy phương trình vô nghiệm