Bài 6: Tính chất của phép cộng các số nguyên

a) Ta có: \(\left|x\right|-\left(-9\right)^3=-100\)

\(\Leftrightarrow\left|x\right|-\left(-729\right)=-100\)

\(\Leftrightarrow\left|x\right|+729=-100\)

\(\Leftrightarrow\left|x\right|=-100-729=-829\)(vô lý)

Vậy: \(x\in\varnothing\)

b) Ta có: \(3x-\left(-10\right)=2x+50\)

\(\Leftrightarrow3x+10-2x-50=0\)

\(\Leftrightarrow x-40=0\)

\(\Leftrightarrow x=40\)

Vậy: x=40

a) Ta có: \(\left|4-5x\right|=24\)

\(\Leftrightarrow\left[{}\begin{matrix}-5x+4=24\\-5x+4=-24\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-5x=20\\-5x=-28\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=\dfrac{28}{5}\end{matrix}\right.\)

Vậy: \(x\in\left\{-4;\dfrac{28}{5}\right\}\)

b) Ta có: \(\left(8+x\right)\left(6-x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+8=0\\6-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-8\\x=6\end{matrix}\right.\)

Vậy: \(x\in\left\{-8;6\right\}\)

a) \(\left|4-5x\right|=24\)

\(\Leftrightarrow\left[{}\begin{matrix}4-5x=24\\4-5x=-24\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=\dfrac{28}{5}\end{matrix}\right.\)

b) \(\left(8+x\right)\left(6-x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}8+x=0\\6-x=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-8\\x=6\end{matrix}\right.\)

a.|4-5.x|=24

TH1: 4-5.x=24

        ⇔5x=-20

        ⇔x=-4

TH1: 4-5.x=-24

        ⇔5x=28

        ⇔x=28/5

b.(8+x).(6-x)=0

\(\left\{{}\begin{matrix}8+x=0\\6-x=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-8\\x=6\end{matrix}\right.\)

\(-152-\left(3x+1\right)=154\)

\(\Leftrightarrow3x+1=-152-154=-306\)

\(\Leftrightarrow3x=-306-1=-307\)

\(\Leftrightarrow x=-\dfrac{307}{3}\)

Ta có: -152-(3x+1)=154

\(\Leftrightarrow-152-3x-1=154\)

\(\Leftrightarrow-3x-153=154\)

\(\Leftrightarrow-3x=307\)

hay \(x=-\dfrac{307}{3}\)

Vậy: \(x=-\dfrac{307}{3}\)

-( 3*x+1)=-152-154

-3*x-1=-306

-3*x=-306+1

X=-305:-3

X=101,7

(-x)+14=12

-x         =12-14

-x         = -2

x          =2

(-x) + 14 =12

-x =12-14

-x=-2

-x =2 => x=2

x = {1;2;3;4;5;6;7;8;9}

y ={1;2;3;4;5;6;7;8;9}

x∈{1;2;3;4;5;6;7;8;9;-1;-2;-3;-4;-5;-6;-7;-8;-9}                                

y∈{1;2;3;4;5;6;7;8;9;-1;-2;-3;-4;-5;-6;-7;-8;-9}

x∈{1;2;3;4;5;6;7;8;9;-1;-2;-3;-4;-5;-6;-7;-8;-9}                                

y∈{1;2;3;4;5;6;7;8;9;-1;-2;-3;-4;-5;-6;-7;-8;-9

a+b= bn thế

a+b=11 => b= 11-a

c+a=2 => c=2-a

b+c= 3 nên 11-a +2-a= 3

11+2-2a=3

13-2a =3

13=3+2a

13-3=2a

10=2a => a=5

Vậy a=5

5+b=11 => b=11-5=6

Vậy b=6

c+5=2 => c=2-5= (-3)

Vậy c= -3

|x|=5

=> x =5 hoặc x= -5

|y|=11

=> y =11 hoặc y= -11

Thay x =5 hoặc y= 11 vào bt x+y, ta có:

5+11=16

Thay x =5 hoặc y= -11 vào bt x+y, ta có:

5-11=-6

Thay x =-5 hoặc y= -11 vào bt x+y, ta có:

-5-11=-16

Thay x =-5 hoặc y= 11 vào bt x+y, ta có:

-5+11=5

Vậy........

\(\left|x\right|=5\)                   \(\left|y\right|=11\)

⇒\(\left[{}\begin{matrix}x=5\\x=-5\end{matrix}\right.\)             ⇒\(\left[{}\begin{matrix}y=11\\y=-11\end{matrix}\right.\)

⇒\(\left[{}\begin{matrix}x+y=5+11=16\\x+y=-5+\left(-11\right)=-16\end{matrix}\right.\)hoặc\(\left[{}\begin{matrix}x+y=5+\left(-11\right)-6\\x+y=\left(-5\right)+11=6\end{matrix}\right.\)

Ta có: 10+9+8+.......+x=10

=>10+9+8+....+x=0

=>(x+9).n=0(n gọi là số các số hạng của vế trái, n khác 0)

=>x+9=0

=>x=-9

Vậy....

239.(-39)+39.139

= 39(239 - 139)

= 39. 100

= 3900

239.(-39+39).139

=239.0.139

=0

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239.(-39) + 39.139

= 39(-239 + 139)

= 39.(-100)

= -3900

|2x - 5| + |30| = 41

=> |2x - 5| + 30 = 41

=> |2x - 5| = 41 - 30 = 11

\(\Rightarrow\left[{}\begin{matrix}2x-5=11\\2x-5=-11\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=11+5=16\\2x=-11+5=-6\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=16:2=8\\x=-6:2=-3\end{matrix}\right.\)

\(\left|2x-5\right|+\left|30\right|=41\) hay \(\left|2x-5\right|+30=41\)

                                   ⇒  \(\left|2x-5\right|=\)41-30=11

                                  \(\Rightarrow\left[{}\begin{matrix}2x-5=11\\2x-5=-11\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=16\\2x=-6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=8\\x-3\end{matrix}\right.\)