Question

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1) | x+2 | = 1
2) | x-3| = -1
3) | x | - x = 2
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Answer 1

a)|x+2|=1

x+2=1

-(x+2)=1

x=1-2=-1

-x-2=1

-x=1+2=3

x=-3


c)|x|-x=2

|-1|+1=2

2=2

x=-1

Answer 2

1) Impartim in doua cazuri posibile: ○ x+2 = 1 x = 1-2  x = -1 ○ -(x+2) = 1 -x-2 = 1 -x = 1+2 -x = 3 x = -3 2) x apartine multimii vide, deoarece modului este intotdeauna pozitiv sau 0. 3) Impartim in doua cazuri posibile: ○ x-x = 2 0 = 2 (fals) => x apartine multimii vide ○-x-x = 2 -2x = 2 x = -1