Question

[Cao Như Ngọc]

1. Tìm số nguyên x, biết

a) x - 43 = ( 35 - x ) - 48

b) 305 - x + 14 = 48 + ( x - 23 )

c) -( x - 6 + 85 ) = ( x + 51 ) - 54

d) -( 35 - x ) - ( 37 - x ) = 33 - x

e) 13 - | x | = | -4 |

f) | x | - 3 + 6 = 16

g) 35 - | 2x - 1 | = 14

h) | 3x - 2 | + 5 = 9 - x

Answer 1

[Nguyễn Lê Phước Thịnh]

a) Ta có: x-43=(35-x)-48

⇔x-43=35-x-48

⇔x-43=-x-13

⇔x-43+x+13=0

⇔2x-30=0

⇔2(x-15)=0

mà 2≠0

nên x-15=0

hay x=15

b) Ta có: 305-x+14=48+(x-23)

⇔319-x=48+x-23

⇔319-x=x+25

⇔319-x-x-25=0

⇔-2x+294=0

⇔-2x=-294

hay x=147

Vậy: x=147

c) Ta có: -(x-6+85)=(x+51)-54

⇔-x+6-85=x+51-54

⇔-x-79=x-3

⇔-x-79-x+3=0

⇔-2x-76=0

⇔-2x=76

hay x=-38

Vậy: x=-38

d) Ta có: -(35-x)-(37-x)=33-x

⇔-35+x-37+x-33+x=0

⇔3x-105=0

⇔3(x-35)=0

mà 3≠0

nên x-35=0

hay x=35

Vậy: x=35

e) Ta có: 13-|x|=|-4|

⇔13-|x|=4

⇔|x|=9

⇔x∈{9;-9}

Vậy: x∈{9;-9}

f) Ta có: |x|-3+6=16

⇔|x|+3=16

⇔|x|=13

hay x∈{-13;13}

Vậy: x∈{-13;13}

g) Ta có: 35-|2x-1|=14

⇔|2x-1|=21

⇔\(\left[{}\begin{matrix}2x-1=21\\2x-1=-21\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=22\\2x=-20\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=11\\x=-10\end{matrix}\right.\)

Vậy: x∈{11;-10}

h) Ta có: |3x-2|+5=9-x

⇔|3x-2|+5-9+x=0

⇔|3x-2|-4+x=0

⇔|3x-2|=0-(-4+x)

⇔|3x-2|=4-x

⇔\(\left[{}\begin{matrix}3x-2=4-x\\3x-2=x-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x-2-4+x=0\\3x-2-x+4=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}4x-6=0\\2x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=6\\2x=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{3}{2}\left(ktm\right)\\x=-1\left(tm\right)\end{matrix}\right.\)

Vậy: x=-1