2)|x|-4=(-1)
3)|x|-(-2)=-1
4)|x|-10=-(-8)
5)|x|+7=12-(-3)
6)|x-2|=4
7)|x+3|=15
8)|x-1|=0
9)|x-5|-7=12
10)|x-7|+13=25
11)|x-3|-16=-4
12)26-|x-9|=-13
13)-7+|x+4|=-3
14)-37-|7-x|=-127
15)|3x+9|-15=27
16)5-|2x-1|=(-7)
17)|x-1|-x+1=0
18)|2-x|+2=x
2)|x|-4=(-1) 3)|x|-(-2)=-1 4)|x|-10=-(-8) 5)|x|+7=12-(-3) 6)|x-2|=4 7)|x+3|=15 8)|x-1|=0 9)|x-5|-7=12 10)|x-7|+13=25 11)|x-3|-16=-4 12)26-|x-9|=-13 13
By Eloise
2) |x|-4=(-1)
|x| = -1 + 4
|x| = 3
⇒ $\left \{ {{x = 3 } \atop {x = -3}} \right.$
3)|x|-(-2)=-1
|x|+2 = -1
|x| = -1 – 2
|x| = -3
⇒ ∅
4)|x|-10=-(-8)
|x| = 8+10
|x| = 18
⇒ $\left \{ {{x = 18 } \atop {x = -18}} \right.$
5)|x|+7=12-(-3)
|x| +7= 15
|x| = 15 – 7
|x| = 8
⇒ $\left \{ {{x = 8 } \atop {x = -8}} \right.$
6)|x-2|=4
⇒ $\left \{ {{x-2=4 } \atop {x-2=-4 }} \right.$ ⇔ $\left \{ {{x = 6 } \atop {x = -2}} \right.$
7)|x+3|=15
⇒ $\left \{ {{x+3=15 } \atop {x+3=-15}} \right.$ ⇔ $\left \{ {{x = 12 } \atop {x = -18}} \right.$
8)|x-1|=0
⇒ x= 1
9)|x-5|-7=12
|x-5| = 12 + 7
|x-5| = 19
⇒ $\left \{ {{x-5=19 } \atop {x-5=-19}} \right.$ ⇔$\left \{ {{x =24 } \atop {x =-14}} \right.$
10)|x-7|+13=25
|x-7| =25-13
|x-7| =12
⇒ $\left \{ {{x-7=12 } \atop {x-7=-12}} \right.$ ⇔ $\left \{ {{x = 19} \atop {x = -5}} \right.$
11)|x-3|-16=-4
|x-3| =-4+16
|x-3| =12
⇒ $\left \{ {{x-3=12 } \atop {x-3=-12}} \right.$ ⇔ $\left \{ {{x = 15 } \atop {x = -9}} \right.$
12)26-|x-9|=-13
|x-9|=26-(-13)
|x-9|=39
⇒ $\left \{ {{x-9=39 } \atop {x-9=-39}} \right.$ ⇔$\left \{ {{x = 48 } \atop {x = -30}} \right.$
13)-7+|x+4|=-3
|x+4|=-3-(-7)
|x+4|=4
⇒ $\left \{ {{x +4=4 } \atop {x+4=-4}} \right.$ ⇔$\left \{ {{x = 0} \atop {x = -8}} \right.$
14)-37-|7-x|=-127
|7-x|=-37-(-127)
|7-x|=90
⇒$\left \{ {{7-x =90 } \atop {7-x=-90}} \right.$ ⇔$\left \{ {{x = -83 } \atop {x = 97}} \right.$
15)|3x+9|-15=27
|3x+9| = 27 + 15
|3x+9| = 42
3x+9 = 42
3x = 42-9
3x = 33
x = 33 : 3 = 11
16)5-|2x-1|=(-7)
|2x-1|=5-(-7)
2x-1 = 12
2x = 12 + 1
2x = 13
x = 13 : 2 = 5,5
17)|x-1|-x+1=0
|x-1|-x = 0-1
|x-1|-x = -1
x-1 = -1+x
⇒ x ∈ Z
18)|2-x|+2=x
|2-x| = x-2
2-x = x-2
⇒ x ∈ Z
Đáp án:
2) |x|-4=(-1)
|x| = -1 + 4
|x| = 3
Vậy: x=3 ; -3
3) |x|-(-2)=-1
|x| + 2 = -1
|x| = -1 – 2
|x| = -3
Vậy: x = ∅
4) |x|-10=-(-8)
|x| = 8+10
|x| = 18
Vậy: x= 18 ; -18
5) |x|+7=12-(-3)
|x| +7= 15
|x| = 15 – 7
|x| = 8
Vậy x = 8 ;-8.
6) |x-2|=4
Vậy: {x-2 = 4}⇒{ x=6}
{x-2 = -4}⇒{ x=-2}
7) |x+3|=15
Vậy: {x+3=15}⇒{x=12}
{x+3=-15}⇒{x=-18}
8)|x-1|=0
Vậy: x= 1
9)|x-5|-7=12
|x-5| = 12 + 7
|x-5| = 19
Vậy: {x-5=19}⇒{x=24}
{x-5=-19}⇒{x=-14}
10)|x-7|+13=25
|x-7| =25-13
|x-7| =12
Vậy: {x−7=12} ⇒ {x=15}
{x−7=−12} ⇒{x=-9}
11)|x-3|-16=-4
|x-3| =-4+16
|x-3| =12
Vậy: {x−3=12} ⇒ {x=15}
{x−3=−12} ⇒{x=-9}
12)26-|x-9|=-13
|x-9|=26-(-13)
|x-9|=39
Vậy: {x−9=39}⇒{x=48}
{x−9=−39} ⇒{x=-30}
13)-7+|x+4|=-3
|x+4|=-3-(-7)
|x+4|=4
Vậy: {x+4=4}⇒{x=8}
{x+4=−4} ⇒{x=0}
14)-37-|7-x|=-127
|7-x|=-37-(-127)
|7-x|=90
Vậy: {7−x=90}⇒{x=-83}
{7−x=−90}⇒{x=97}
15)|3x+9|-15=27
|3x+9| = 27 + 15
|3x+9| = 42
3x+9 = 42
3x = 42-9
3x = 33
x = 33 : 3
x = 11
16)5-|2x-1|=(-7)
|2x-1|=5-(-7)
2x-1 = 12
2x = 12 + 1
2x = 13
x = 13 : 2
x = 5,5
17)|x-1|-x+1=0
|x-1|-x = 0-1
|x-1|-x = -1
x-1 = -1+x
Vậy: x ∈ Z
18)|2-x|+2=x
|2-x| = x-2
2-x = x-2
Vậy: x ∈ Z
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