1) –45 + 5.(–2x) = 95
2) x.(12 + x).(71 – x) = 0
3) (x – 11).(x + 12).(–x – 13) = 0
4) |2.x – 15| = 7
5) –2.|x + 32| = –112
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\(1\)) \(5-\left(10-x\right)=7\)
\(10-x=5-7\)
\(10-x=-2\)
\(x=10-\left(-2\right)\)
\(x=12\)
\(2\)) \(-32-\left(x-5\right)=0\)
\(x-5=-32-0\)
\(x-5=-32\)
\(x=-32+5\)
\(x=-27\)
1/ x2-3x+2=0
⇒ (x2-2x)-(x-2)=0
⇒ x(x-2)-(x-2)=0
⇒ (x-1)(x-2)=0
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
2) x2-6x+5=0
⇒x2-6x+9-4=0
⇒(x2-6x+9)-22=0
⇒(x-3)2-22=0
⇒(x-3-2)(x-3+2)=0
⇒(x-5)(x-1)=0
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x-5=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=5\end{matrix}\right.\)
3) 2x2+5x+3=0
⇒ (2x2+2x)+(3x+3)=0
⇒ 2x(x+1)+3(x+1)=0
⇒ (x+1)(2x+3)=0
\(\Rightarrow\left[{}\begin{matrix}x+1=0\\2x+3=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-1\\x=-1,5\end{matrix}\right.\)
4) x2-8x+15=0
⇒ (x2-8x+16)-1=0
⇒ (x-4)2-12=0
⇒ (x-4-1)(x-4+1)=0
⇒ (x-5)(x-3)=0
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x-5=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=5\end{matrix}\right.\)
5) x2-x-12=0
⇒ (x2-4x)+(3x-12)=0
⇒ x(x-4)+3(x-4)=0
⇒ (x-4)(x+3)=0
\(\Rightarrow\left[{}\begin{matrix}x+3=0\\x-4=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-3\\x=4\end{matrix}\right.\)
1: Ta có: \(x^2-3x+2=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
2: Ta có: \(x^2-6x+5=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=5\end{matrix}\right.\)
3: Ta có: \(2x^2+5x+3=0\)
\(\Leftrightarrow\left(x+1\right)\left(2x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-\dfrac{3}{2}\end{matrix}\right.\)
4: Ta có: \(x^2-8x+15=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=5\end{matrix}\right.\)
5: Ta có: \(x^2-x-12=0\)
\(\Leftrightarrow\left(x-4\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-3\end{matrix}\right.\)
1) 10 - 3 ( x - 1 ) = -5
3 ( x - 1 ) = 10 - ( - 5 )
3 ( x - 1 ) = 15
x - 1 = 15 : 3
x - 1 = 5
x = 5 + 1
x = 6
2) 3x + 75 = - 15
3x = - 15 - 75
3x = - 90
x = -90 : 3
x = -30
4) 12 - ( x - 7 ) = - 8
x - 7 = 12 - (- 8 )
x - 7 = 20
x = 20 + 7
x = 27
5) x + 75 = 15
x = 15 - 75
x = -60
7) 2x + 18 = 10
2x = 10 - 18
2x = -8
x = - 8 : 2
x = -4
8) 26 - 3x = 5
3x = 26 - 5
3x = 21
x = 21: 3
x = 7
9) x - 12 = - 15
x = -15 + 12
x =-3
10 ) 24 - 2 ( x + 5 ) = 38
2 ( x+ 5 ) = 24 - 38
2 ( x + 5 ) = - 14
x + 5 = -14 : 2
x + 5 = -7
x = -7 - 5
x = -12
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1) \(\left(x-2\right)\left(x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x+4=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-4\end{matrix}\right.\)
2) \(\left(x-2\right)\left(x+15\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x+15=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-15\end{matrix}\right.\)
3) \(\left(7-x\right)\left(x+19\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}7-x=0\\x+19=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=7\\x=-19\end{matrix}\right.\)
4) \(-5< x< 1\)
\(\Rightarrow x\in\left\{-1;-3;-2;-1;0\right\}\)
5) \(\left(x-3\right)\left(x-5\right)< 0\)
\(\Rightarrow\left[{}\begin{matrix}x-3>0\\x-5< 0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x>3\\x< 5\end{matrix}\right.\)
\(\Rightarrow3< x< 5\)
6) \(2x^2-3=29\)
\(\Rightarrow2x^2=29+3\)
\(\Rightarrow2x^2=32\)
\(\Rightarrow x^2=\dfrac{32}{2}\)
\(\Rightarrow x^2=16\)
\(\Rightarrow x^2=4^2\)
\(\Rightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)
7) \(-6x-\left(-7\right)=25\)
\(\Rightarrow-6x+7=25\)
\(\Rightarrow-6x=25-7\)
\(\Rightarrow-6x=18\)
\(\Rightarrow x=\dfrac{18}{-6}\)
\(\Rightarrow x=-3\)
8) \(46-\left(x-11\right)=-48\)
\(\Rightarrow x-11=48+46\)
\(\Rightarrow x-11=94\)
\(\Rightarrow x=94+11\)
\(\Rightarrow x=105\)
1: (x-2)(x+4)=0
=>x-2=0 hoặc x+4=0
=>x=2 hoặc x=-4
2: (x-2)(x+15)=0
=>x-2=0 hoặc x+15=0
=>x=2 hoặc x=-15
3: (7-x)(x+19)=0
=>7-x=0 hoặc x+19=0
=>x=7 hoặc x=-19
4: -5<x<1
=>\(x\in\left\{-4;-3;-2;-1;0\right\}\)
5: (x-3)(x-5)<0
=>x-3>0 và x-5<0
=>3<x<5
6: 2x^2-3=29
=>2x^2=32
=>x^2=16
=>x=4 hoặc x=-4
7: -6x-(-7)=25
=>-6x=25-7=18
=>x=-3
8: 46-(x-11)=-48
=>x-11=46+48=94
=>x=94+11=105
Bài 2 : Tính
1/ (-15)-/-10/+/-9/-/-5/
=-15-10+9-5
=-21
2/14-(-13)-(-21)+(-32)
=14+13+21-32
=16
3/(-12)-(-17)-(-21)+(-32)
= -12+17+21-32
=-6
4/-/-14/ + /-10/-(-12)+(-8)
=-14+10+12-8
=0
5/-(-11)+(-15)+(+13)-21
=11-15+13-21
=-12
c: Ta có: 11+x:5=13
\(\Leftrightarrow x:5=2\)
hay x=10
d: Ta có: \(13+2\left(x+1\right)=15\)
\(\Leftrightarrow2x+2=2\)
\(\Leftrightarrow2x=0\)
hay x=0
e: Ta có: 2x+21=41
\(\Leftrightarrow2x=20\)
hay x=10
f: Ta có: \(12+3\left(x-2\right)=60\)
\(\Leftrightarrow3\left(x-2\right)=48\)
\(\Leftrightarrow x-2=16\)
hay x=18
g: Ta có: \(24x-11\cdot13=11\cdot11\)
\(\Leftrightarrow24x=11\cdot24\)
hay x=11
h: Ta có: \(17-\left(x-4\right):2=3\)
\(\Leftrightarrow\left(x-4\right):2=14\)
\(\Leftrightarrow x-4=28\)
hay x=32