Question

Rezolvati in multimea numerelor intregi urmatoarele ecuatii:
a) 2x + 1 =-7
b)3x-1=-13
c)2x+15 =5
d)2x+10=0
e)3x+24=0
f)-2x+1=-7
g)-3x+1=-14
h)-5x+1=1
i)3+2x=-7
j)5+2x =-11
k)6+3x=-54
l) 1+9x=-89
m)1-2x=-7
n)5-4x=-3
o) 1-6x=-11
p)1-5x=-19

Answer 1

Răspuns:

Explicație pas cu pas:

a)

2 x + 1 = - 7

2 x = - 7 - 1

2 x = - 8

x = ( - 8 ) : 2

x = - 4

Verific:

2 x + 1 = 2 × ( - 4 ) + 1 = - 8 + 1 = - 7

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b)

3 x - 1 = - 13

3 x = - 13 + 1

3 x = - 12

x = ( - 12) : 3

x = - 4 ∈ Z

Verific:

3 x - 1 = 3 × ( - 4 ) - 1 = - 12 - 1 = - 13

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c)

2 x + 15 = 5

2 x = 5 - 15

2 x = - 10

x = ( - 10) : 2

x = - 5

Verific:

2 x + 15 = 2 × ( - 5 ) + 15 = - 10 + 15 = 5

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d)

2 x + 10 = 0

2 x = 0 - 10

2 x = - 10

x = ( - 10 ) : 2

x = - 5 ∈ Z

Verific:

2 x + 10 = 2 × ( - 5 ) + 10 = - 10 + 10 = 0

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e)

3 x + 24 = 0

3 x = - 24

x = ( - 24 ) : 3

x = - 8

Verific:   3 x + 24 = 3 × ( - 8 ) + 24 = - 24 + 24 = 0

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f)

- 2 x + 1 = - 7

- 2 x = - 7 - 1

- 2 x = - 8

x = ( - 8 ) : ( - 2 )

x = 4

Verific:    - 2 x + 1 = ( - 2 ) × 4 + 1 = - 8 + 1 = - 7

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g)

- 3 x + 1 = - 14

- 3 x = - 14 - 1

- 3 x = - 15

x = ( - 15 ) : ( - 3 )

x = 5 ∈ Z

Verific:    - 3 x + 1 = - 3 × 5 + 1 = - 15 + 1 = - 14

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h)

- 5 x + 1 = 1

- 5 x = 1 - 1

- 5 x = 0 ⇒   x = 0 : ( - 5)  ⇒   x = 0

Verific:   - 5 x + 1 = - 5 × 0 + 1 = 0 + 1 = 1

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i)

3 + 2 x = - 7

2 x = - 7 - 3

2 x = - 10

x = ( - 10 ) : 2

x = - 5

Verific:   3 + 2 x = 3 + 2 × ( - 5 ) = 3 - 10 = - 7

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j)

5 + 2 x = - 11

2 x = - 11 - 5

2 x = - 16

x = ( - 16 ) : 2

x = - 8 ∈  Z

Verific:   5 + 2 x = 5 + 2 × ( - 8 ) = 5 - 16 = - 11

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k)

6 + 3 x = - 54

3 x = - 54 - 6

3 x = - 60

x = ( - 60 ) : 3

x = - 20

Verific:    6 + 3 x = 6 + 3 × ( - 20 ) = 6 - 60 = - 54

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l)

1 + 9 x = - 89

9 x = - 89 - 1

9 x = - 90

x = ( - 90 ) : 9

x = - 10

Verific:     1 + 9 x = 1 + 9 × ( - 10 ) = 1 - 90 = - 89

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m)

1 - 2 x = - 7

- 2 x = - 7 - 1

- 2 x = - 8

x = ( - 8 ) : ( - 2 )

x = 4

Verific:      1 - 2 x = 1 - 2 × 4 = 1 - 8 = - 7

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n)

5 - 4 x = - 3

- 4 x = - 3 - 5

- 4 x = - 8

x = ( - 8 ) : ( - 4 )

x = 2 ∈ Z

Verific:      5 - 4 x = 5 - 4 × 2 = 5 - 8 = - 3

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o)

1 - 6 x = - 11

- 6 x = - 11 - 1

- 6 x = - 12

x = ( - 12) : ( 6)

x = 2  ∈ Z

Verific:      1 - 6 x = 1 - 6 × 2 = 1 - 12 = - 11

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p)

1 - 5 x = - 19

- 5 x = - 19 - 1

- 5 x = - 20

x = ( - 20 ) : ( - 5)

x = 4 ∈ Z

Verific:   1 - 5 x = 1 - 5 × 4 = 1 - 20 = - 19