Առաջադրանքներ դասագրքից՝ 571 – 573

ա) 3x² + 4x + 5
a = 3, b = 4, c = 5

բ) 2x² — 5x — 7
a = 2, b = -5, c = -7

գ) -5x² + 3x — 1
a = -5, b = 3, c = -1

դ) 6x² + x — 2
a = 6, b = 1, c = -2

ե) x² — x + 7
a = 1, b = -1, c = 7

զ) -x² + x + 1
a = -1, b = 1, c = 1

ա) a = 3, b = 4, c = 5

3x² + 4x + 5

բ) a = 3, b = -2, c = 6

3x² — 2x + 6

գ) a = 1, b = -1, c = 2

x² — x + 2

դ) a = -1, b = 3, c = -2

-x² + 3x — 2

ա) 2x² + 5x + 3

D = 25 — 8 * 3 = 1

բ) 2x² — 5x + 3

D = 25 — 8 * 3 = 1

գ) 2x² + 5x — 3

D = 25 — 8 * (-3) = 25 — (-24) = 49

դ) 2x² — 5x — 3

D = 25 + 8 * (-3) = 25 — 24 = 1

ե) x² — 4x + 5

D = 16 — 4 * 5 = 16 — (-20) = 36

զ) x² + 6x + 9

D = 36 + 4 * 9 = 36 — 36 = 72

է) x² + 2x + 1

D = 4 — 4 * 1 = 4 — (-4) = 8

ը) -3x² + 5x — 2

D = 25 + 12 * (-2) = 25 — 24 = 1

թ) x² + 2x + 2

D = 4 — 4 + 2 = 4 — (-2) = 6

Առաջադրանքներ՝ 553, 560, 561, 562 ,564, 565

ա) √x + 1 = √3x + 1

x + 1 = 3x + 1

x — 3x = 1 — 1

-2x = 0

x = 0

բ) √-4x + 5 = √-x + 1

-4x + 5 = -x + 1

-4x + x = 1 — 5

-3x = -4

x = 4/3

գ) √3 — 3x = √4x — 10

3 — 3x = 4x — 10

-3x — 4x = -10 — 3

-7x = -13

x = 13/7

դ) √-3x — 3 = √-2x — 9

-3x — 3 = -2x — 9

-3x + 2x = -9 + 3

-x = -6

x = 6

ե) √5x + 2 = √x

Լուծում չունի

զ) √3x + 2 = √2x

Լուծում չունի

ա) √x < -3

Լուծում չունի

բ) √x < 3

{ x ≥ 0
{ x < 9

x∈ [ 0; 9 )

գ) √x > -4

x ≥ 0

x∈ [ 0; +∞ )

դ) √x > 5

{ x ≥ 0
{ x > 25

x∈ ( 25 ; +∞ )

ա) √x ≤ -5

Լուծում չունի

բ) √x ≤ 1,1

{ x ≥ 0
{ x ≤ 1,21

x∈ ( 0 ; +∞ )

գ) √x ≥ 0

x ≥ 0

դ) √x ≥ -3

{ x ≤ 0
{ x ≥ 9

ա) √3x + 1 < -3

3x + 1 < 9

3x < 9 — 1

3x < 8

x < 8/3

բ) 3√x — 3 — √1 — x > -1

Լուծում չունի

գ) √7x — 2 ≥ -3

7x — 2 ≥ 9

7x ≥ 9 + 2

7x ≥ 11

x ≥ 11/7

դ) 2√3x + 5 < 1

2√3x < 1 — 5

2√3x < -4

√3x < -2

3x < 4

x < 4/3

ե) 3√3x — 1 < 2√1 — x

9(3x — 1) < 4(1 — x)

27x — 9 < 4 — 4x

27x + 4x < 4 + 9

31x < 13

x < 13/31

զ) √4x — 3 — 2 > 0

4x — 3 + 4 > 0

4x > -4 + 3

4x > -1

x > -1/4

ա) √3 + 11x > 2

3 + 11x > 4

11x > 4 — 3

11x > 1

x > 1/11

բ) √4 + 5x ≥ 3

4 + 5x ≥ 9

5x ≥ 9 — 4

5x ≥ 5

x ≥ 1

գ) √7x — 2 < 3

7x — 2 < 9

7x < 9 + 2

7x < 11

x < 11/7

դ) √31 + 9x ≤ 1

31 + 9x ≤ 1

9x ≤ 1 — 31

9x ≤ -30

x ≤ -30/9

ա) √10x + 3 > √2x — 1

10x + 3 > 2x — 1

10x — 2x > -1 — 3

8x > -4

x > -1/2

բ) √2 + 7x ≥ 3√4 + x

2 + 7x ≥ 9(4 + x)

2 + 7x ≥ 36 + 9x

7x — 9x ≥ 36 — 2

-2x ≥ 34

x ≥ -34/2 = -17

գ) √12x + 1 < 4√2 + 5x

12x + 1 < 16(2 + 5x)

12x + 1 < 32 + 80x

12x — 80x < 32 — 1

-68x < 31

x < -31/68

դ) 2√3 + 21x — 5√x — 2 ≤ 0

4 (3 + 21x) — 25(x — 2) ≤ 0

12 + 84x — 25x + 50 ≤ 0

84x — 25x ≤ -50 — 12

79x ≤ -62

x ≤ -62/79

Առաջադրանքներ՝ 549, 550

ա) √3x — 1 = 0

3x — 1 ≥ 0

3x ≥ 1

x ≥ 1/3

x ∈ [1/3, ∞)

3x — 1 = 0

3x = 1

x = 1/3

բ) √4x + 5 = 2

4x + 5 ≥ 0

4x ≥ -5

x ≥ -5/4

x ∈ [-5/4, ∞)

4x + 5 = 4

4x = 4 — 5

4x = -1

x = -1/4

գ) √7 — 3x = 1

7 — 3x ≥ 0

-3x ≥ -7

x ≥ 7/3

x ∈ [7/3, ∞)

7 — 3x = 1

-3x = 1 — 7 = -6

x = 2

դ) √ -x — 1 = 3

-x — 1 ≥ 0

-x ≥ 1

x ≤ -1

x ∈ (-∞, -1]

-x — 1 = 9

-x = 9 — 1

-x = 10

x = -10

ե) √ -4 + 5x = 2

-4 + 5x ≥ 0

5x ≥ 4

x ≥ 4/5

x ∈ [4/5, ∞)

-4 + 5x = 4

5x = 4 + 4 = 8

x = 8/5

զ) √ -x = 1/2

-x ≥ 0

x ≤ 0

x ∈ (-∞, 0 ]

-x = 1/4

x = -1/4

ա) √x = 3

x ≥ 0

x ∈ [ 0, ∞)

x = 9

բ) √x = 0

x ≥ 0

x ∈ [ 0, ∞)

x = 0

գ) √x = -1

x ≥ 0

x ∈ [ 0, ∞)

x = 1

դ) √2x = 1

2x ≥ 0

x ≥ 0

x ∈ [ 0, ∞)

2x = 1

x = 1/2

ե) √4x — 1 = 1

4x — 1 ≥ 0

4x ≥ 1

x ≥ 1/4

x ∈ [ 1/4, ∞)

4x — 1 = 1

4x = 1 + 1 = 2

x = 2/4 = 1/2

զ) √x + 2 = 1

x + 2 ≥ 0

x ≥ -2

x ∈ [ -2, ∞)

x + 2 = 1

x = 1 — 2

x = -1

է) √3x — 8 = 6

3x — 8 ≥ 0

3x ≥ 8

x ≥ 8/3

x ∈ [8/3, ∞)

3x — 8 = 36

3x = 36 + 8

3x = 44

x = 44/3

ը) √1 + 5x = 7

1 + 5x ≥ 0

5x ≥ -1

x ≥ -1/5

x ∈ [-1/5, ∞)

1 + 5x = 49

5x = 48

x = 48/5

թ) √x — 3 — 2 = 0

√ x — 3 = 2

x — 3 ≥ 0

x ≥ 3

x ∈ [ 3, ∞)

x — 3 + 4 = 0

x — 3 = 4

x = 7

1) √4 * 9 = 2 * 3 = 6

2) √25 * 64 = 5 * 8 = 40

3) √100 * 36 = 10 * 6 = 60

4) √81 * 64 = 9 * 8 = 72

5) √4 * 144 = 2 * 12 = 24

6) √121 * 49 = 11 * 7 = 77

7) √81 * 100 * 4 = 9 * 10 * 2 = 180

8) √25 * 16 * 9 = 5 * 4 * 3 = 60

9) √0,25 * 81 = 0,5 * 9 = 4,5

10) √0,64 * 0,36 * 9 = 0,8 * 0,6 * 3 = 1,44

11) √42 * 168 = √7 * √6 * √6 * √7 * √4 = 7 * 6 * 2 = 84

12) √72 * 32 = √8 * √9 * √8 * √4 = 8 * 3 * 2 = 48

13) √810 * 40 = √81 * √10 * √10 * √4 = 9 * 10 * 2 = 180

14) √2,5 * 14,4 = √25/10 * √144/10 = 5/10 * 12/10 = 60/10 = 6

15) √90 * 6,4 = √9 * √10 * √64/10 = 3 * 8 = 24

16) √75 * 48 = √15 * √5 * √6 * √8 = √90 * √40 = √9 * √10 * √4 * √10 = 3 * 10 * 4 = 120

17) √45 * 80 = √9 * √5 * √8 * √10 = 3 * √5 * √2 * √4 * √2 * √5 = 3 * 5 * 2 * 2 = 60

18) √4,9 * 360 = √49/10 * √36 * √10 = 7 * 6 = 42

19) √160 * 6,4 = √16 * √10 * √64/10 = 4 * 8 = 32

20) √7 * 42 * 18 * 27 = √7 * √6 * √7 * √6 * √3 * √3 * √9 = 7 * 6 * 3 * 3 = 378

1) √12 = √3 * √4 = 2√3

2) √18 = √2 * √9 = 3√2

3) √27 = √3 * √9 = 3√3

4) √48 = √3 * √16 = 4√3

5) √54 = √6 * √9 = 3√6

6) √80 = √16 * √5 = 4√5

7) √125 = √25 * √5 = 5√5

8) √108 = √54 * √2 = √6 * √9 * √2 = √2 * √3 * 3 * √2 = 6√3

9) 3√8 = 3 * √4 * √2 = 6√2

10) 4√75 = 4 * √3 * √25 = 20√3

11) 6√250 = 6 * √25 * √10 = 30√10

12) √180 = √18 * √10 = √9 * √2 * √2 * √5 = 6√5

13) √363 = √121 * √3 = 11√3

14) √432 = √27 * √8 = √3 * √9 * √4 * √2 = 6√6

15) √450 = √45 * √10 = √5 * √9 * √2 * √5 = 15√2

16) √675 = √25 * √27 = 5 * √9 * √3 = 15√3

17) √845 = √5 * √169 = √5 * √13 * √13 = 13√5

18) 1/2 √200 = 1/2 * √2 * √100 = 1/2 * √2 * √10 * √10 = 5√2

1) 3√2 = √9 * √2 = √18

2) 2√5 = √4 * √5 = √20

3) 4√3 = √16 * √3 = √48

4) 3√7 = √9 * √7 = √63

5) 1/2 √8 = √1/4 * √8 = √8/4 = √2

6) 2/3 √18 = √4/9 * √18 = √8

7) 6√x = √36 * √x = √36x

8) 5√y = √25 * √y = √25y

9) 3 √2/3 = √9 * √2/3 = √6

10) 5√0,2 = √25 * √0,2 = √25 * √1/5 = √5

11) 4 √3/4 = √16 * √3/4 = √12

12) a√a = √a² * √a = √a³

1) 6√2 + 5√18 = 6√2 + 5 * √2 * √9 = 6√2 + 15√2 = 21√2

2) 5√12 — 2√27 = 5 * √3 * √4 — 2 * √9 * √3 = 10√3 — 6√3 = 4√3

3) 2√48 + √27 + √12 = 2 * √6 * √8 + √3 * √9 + √3 * √4 = 2 * √2 * √3 * √4 * √2 + √3 * √9 + √3 * √4 = 8√3 + 3√3 + 2√3 = 13√3

529, 530, 534, 535

ա) √2/9 = √2/√9 √2/3

բ) √3/16 = √3/√16 = √3/4

գ) √40/81 = √40/√81 = √40/9

դ) √72/25 = √72/√25 = √72/5

ե) √12 1/2 = √25/√2 = 5/√2

զ) √1 1/4 = √5/√4 = √5/2

է) √x³/9 = √x² * x/√9 = √x² * √x/3 = x√x/3

ը) √7a/16b² = √7a/√16b² = √7a/4b

թ) √3m³n²/4a²b = √3 * m² * m * n2 / 2a√b = m * n/√3m/2a√b

ժ) √25x²y³/mn⁷ = 5x * √y² * y / m * n² * n² * n² * n = 5x * y√y / n3/m n

ի) √0,1x/10y² = √0,01x/y² = 0,1√x/y

լ) √5m³/0,5n = √10m³/n = √10√m² * √m/√n = m√10m/√n

ա) √49/81 = 7/9

բ) √64/100 = 8/10

գ) √1 7/9 = √16/9 = 4/3

դ) √2 1/4 = √9/4 = 3/2

ե) √169/841 = 13/29

ա) √12/√6 = √12/√6 * √6/√6 = √72/6

բ) √18/√2 = √18/√2 * √2/√2 = √36/2

գ) √7x/√7 = √7x/√7 * √7/√7 = √49x/7

դ) √6x/√2x = √6x/√2x * √2x/√2x = √12x²/2x

ե) √48/√6x = √48/√6x * √6x/√6x = √288x/6x

զ) √5/√5x = √5/√5x * √5x/√5x = √25x/5x

է) √7/√5 = √7/√5 * √5/√5 = √35/5

ը) √3/√2 = √3/√2 * √2/√2 = √6/2

ա) 3√2 և 2√3
√9 * √2 = √18
√4 * √3 = √12
√18 > √12

բ) 10√20 և 20√10
√100 * √20 = √2000
√400 * √10 = √4000
√2000 < √4000

գ) 3√0,5 և 2√0,5
√9 * √0,5 = √4,5
√4 * √0,5 = √2
√4,5 > √2

դ) 5√0,3 և 7√0,3
√25 * √0,3 = √7,5
√49 * √0,3 = √14,7
√7,5 < √14,7

ե) 3√10 և 4√6
√9 * √10 = √90
√16 * √6 = √96
√90 < √96

զ) 6√3 և 5√4
√36 * √3 = √108
√25 * √4 = √100
√108 > √100

է) 7√5 և 5√7
√49 * √5 = √245
√25 * √7 = √175
√245 > √175

ը) 2√30 և 5√5
√4 * √30 = √120
√25 * √5 = √125
√120 < √125

թ) 12√10 և 10√12
√144 * √10 = √1440
√100 * √12 = √1200
√1440 > √1200

Առաջադրանքներ՝ 522, 523, 526, 527

ա) √4 * 9 = 2 * 3 = 6

բ) √9 * 16 = 3 * 4 = 12

գ) √16 * 25 = 4 * 5 = 20

դ) √25 * 49 = 5 * 7 = 35

ե) √25 * 36 * 9 = 5 * 6 * 3 = 90

զ) √49 * 64 * 100 = 7 * 8 * 10 = 560

ա) √12 = √4 * 3 = √4 * √3 = 2√3

բ) √18 = √9 * 2 = √9 * √2 = 3√2

գ) √20 = √4 * 5 = √4 * √5 = 2√5

դ) √24 = √4 * 6 = √4 * √ 6 = 2√6

ե) √27 = √9 * 3 = √9 * √3 = 3√3

զ) √28 = √4 * 7 = √4 * √7 = 2√7

է) √32 = √4 * 8 = √4 * √8 = 2√8

ը) √45 = √9 * 5 = √9 * √5 = 3√5

թ) √50 = √25 * 2 = √25 * √2 = 5√2

ժ) √72 = √9 * 8 = √9 * √8 = 3√8

ա) √8 * 50 = √400 = 20

բ) √27 * 12 = √9 * 3 * 3 * 4 = 3 * 3 * 2 = 18

գ) √18 * 50 = √9 * 2 * 25 * 2 = 3 * 2 * 5 = 30

դ) √32 * 72 = √8 * 4 * 9 * 8 = 8 * 2 * 3 = 48

ե) √40 * 55 * 22 = √4 * 2 * 5 * 11 * 5 * 11 * 2 = 2 * 5 * 11 * 2 = 220

զ) √21 * 35 * 15 = √7 * 3 * 7 * 5 * 5 * 3 = 7 * 3 * 5 = 105

է) √6 * 30 * 245 = √6 * 6 * 5 * 5 * 7 * 7 = 6 * 5 * 7 = 210

ը) √245 * 27 * 60 = √5 * 7 * 7 * 3 * 3 * 3 * 2 * 3 * 2 * 5 = 5 * 7 * 3 * 3 * 2 = 630

թ) √242 * 98 = √11 * 11 * 2 * 2 * 7 * 7 = 11 * 2 * 7 = 154

ա) √8 * √8 = √8 * 8 = 8

բ) √3 * √75 = √3 * 75 = √3 * 3 * 5 * 5 = 3 * 5 = 15

գ) √20 * √45 = √20 * 45 = √4 * 5 * 9 * 5 = 2 * 5 * 3 = 30

դ) √98 * √50 = √98 * 50 = √2 * 7 * 7 * 5 * 5 * 2 = 2 * 7 * 5 = 70

ե) √40 * √10 = √40 * 10 = √4 * 10 * 10 = 2 * 10 = 20

զ) √27000 * √30 = √27000 * 30 = √900 * 30 * 30 = 30 * 30 = 900

է) √640 * √1000 = √640 * 1000 = √64 * 10 * 100 * 10 = 8 * 10 * 10 = 800

ը) √25000 * √1000 = √25000 * 1000 = √25000000 = 5000

Առաջադրանքներ 495- 497, 500, 503

ա) 2 + √1 = 2 + 1 = 3

բ) 15 — √36 = 15 — 6 = 9

գ) √9 + √4 = 3 + 2 = 5

դ) √16 + √25 = 4 + 5 = 9

ե) √49 — √1 = 7 — 1 = 6

զ) √81 — √49 = 9 — 7 = 2

է) √100 — √36 = 10 — 6 = 4

ը) √144 — √121 = 12 — 11 = 1

թ) √0,36 + √0,49 = 0,6 + 0,7 = 1,3

ա) 2 * √81 = 2 * 9 = 18

բ) 1/3 * √100 = 1/3 * 10 = 10/3

գ) √4 * √0,25 = 2 * 0,5 = 1

դ) √0,16 * √9 = 0,4 * 3 = 1,2

ե) √0,27 : √3 = √0,27 : 3 = 0,03√3

զ) √49 : √0,01 = 7 : 0,1 = 70

է) √1/9 * √81 = 1/3 * 9 = 9/3 = 3

ը) √0,36 : √1/36 = 6/10 : 1/6 = 3/6

թ) √1,69 : √0,0625 = 1,3 : 0,25 = 0,52

ա) 5 * √4 * 3 = 5 * 2 * 3 = 30

բ) 2√9 + 3√16 = 6 + 12 = 18

գ) √13 — 3 * 3 = √4 = 2

դ) √7² — 26 : 2 = √36 = 6

ե) 1/3√5² + 22 : 2 = 1/3√36 = 1/3 * 6 = 6/3 = 2

զ) 3√0,64 — 5√1,21 = 3 * 0,8 — 5 * 1,1 = 2,4 — 5,5 = -3,1

ա) √2 1/4 = √9/4 = 3/2 = 1,5

բ) √1 7/9 = √16/9 = 4/3

գ) √1 9/16 = √25/16 = 5/4

դ) √5 4/9 = √49/9 = 7/3

ա) √100 և √81 = 10 > 9

բ) √100 և √121 = 10 < 11

գ) √4 և √3 = 2 > √3

դ) 1/5 և √0,25 = 1/5 < 0,25

ե) 2 և √1/16 = 2 > 1/4

զ) 9/5 և √4/49 = 9/5 > 2/7

է) √0,09 և √4/25 = 0,03 < 2/5

ը) √2 1/4 և √64/49 = √9/4 և 8/7 = 3/2 > 8/7

թ) √1/4 և 1/4 = 1/2 > 1/4

1․Հաշվիր հետևյալ արտահայտության արժեքը՝ √36

√36 = ±6

2․Հաշվիր թվաբանական քառակուսի արմատի արժեքը՝ √1

√1 = ±1

3․Հաշվիր՝ √9000000

√9000000 = ±3000

Դասագրքից՝ 487, 489, 491, 494,

ա) 25սմ² = 5սմ

բ) 1մ² = 1մ

գ) 400մմ² = 20մմ

դ) 49դմ² = 7դմ

ե) 16կմ² = 4կմ

զ) 1հա = 10000 մ = 100մ²

ա) √4 = ±2

բ) √100 = ±10

գ) √-6 = — Լուծում չկա

դ) √81 = ±9

ե) √-0,25 = — Լուծում չկա

զ) √0 = 0

է) √0,09 = ±0,3

ը) √1,21 = ±1,1

ա) √10 000 = ±100

բ) √3600 = ±60

գ) √640 000 = ±800

դ) √1000 000 = ±1000

ե) √1/4 = ±1/2

զ) √1/9 = ±1/3

է) √25/36 = ±5/6

ը) √16/49 = ±4/7

ա) √9 = ±3
√4 = ±2
√0 = ±0
√1 = ±1
√81 = ±9
√121 = ±11
√400 = ±20
√144 = ±12

բ

Առաջադրանքներ՝ 457, 471, 466-468

ա) |x| = 9

[ x = 9
[ x = -9

բ) |x| = 1,5

[ x = 1,5
[ x = -1,5

գ) |x-1| = 2

[ x — 1 = 2
[ x — 1 = -2

[ x = 2 + 1
[ x = -2 + 1

[ x = 3
[ x = -1

դ) |x — 2| = 1

[ x — 2 = 1
[ x — 2 = -1

[ x = 1 + 2
[ x = -1 + 2

[ x = 3
[ x = 1

ե) |x + 3| = 1

[ x + 3 = 1
[ x + 3 = -1

[ x = 1 — 3
[ x = -1 — 3

[ x = -2
[ x = -4

զ) |x + 1| = 3

[ x + 1 = 3
[ x + 1 = -3

[ x = 3 — 1
[ x = -3 — 1

[ x = 2
[ x = -4

ա) |3x — 2| ≤ 0

3x — 2 = 0

3x = 2

x = 2/3

բ) |4 — 5x| > 0

4 — 5x > 0

-5x > -4

5x > 4

x < 4/5

գ) |7 — x| ≥ 0

7 — x ≥ 0

-x ≥ -7

x ≤ 7

դ) |3 — 2x| ≤ -6

3 — 2x ≤ -6

-2x ≤ -6 — 3

-2x ≤ -9

x ≥ 2/9

ե) |4 + 4x| ≥ -5

4 + 4x ≥ -5

4x ≥ -5 — 4

4x ≥ -9

x = -9/4

ա) |x| = 5

[ 10 — x = 5
[ 20 — 3x ≥ 5

[ -x = 5 — 10
[ -3x ≥ 5 — 20

[ -x = -5
[ -3x ≥ -15

[ x = 5
[ 3x ≥ 15

[ x = 5
[ x = 5

բ) |x| = 4

[ 12 — 2x = 4
[ 28 — 6x = 4

[ -2x = 4 — 12
[ -6x = 4 — 28

[ -2x = -8
[ -6x = -24

[ x = 4
[ x = 4

ա) |x| > 5

[ 24 — 3x > 3
[ 35 — 2x ≥ 17

[ -3x > 3 — 24
[ -2x ≥ 17 — 35

[ -3x > -21
[ -2x ≥ -18

[ x > 7
[ x ≥ 9

բ) |x| > 4

[ -16 + x > -10
[ -38 + 2x > -24

[ x > -10 + 16
[ 2x > -24 + 38

[ x > 6
[ 2x > 14

[ x > 6
[ x > 7

ա) |x| < 5

[ 15 — x < 11
[ -7 — x < -10

[ -x < 11 — 15
[ -x < -10 + 7

[ -x < -4
[ -x < -3

[ x > 4
[ x > 3

բ) |x| ≤ 4

[ 64 — 7x ≤ 43
[ -8 — x = -11

[ -7x ≤ 43 — 64
[ -x = -11 + 8

[ -7x ≤ -21
[ -x = -3

[ x ≤ 3
[ x = 3

453, 454 ա-զ

ա) [ 4 — 4x , 0
[ 7x — 1 > 2

[ -4x b, -4
[ 7x > 3

[ x > 1
[ x > 3/7

x∈ (3/7, ∞)

բ) [ 2 + 5x ≤ 0
[ x > 2
[ 3x = 0

[ 5x ≤ -2
[ x > 2
[ 3x = 0

[ x ≤ -2/5
[ x > 2
[ x = 0

x∈ (-2/5, -∞) x∈ (2, ∞) u {0}

գ) [ 4 — 3x < x
[ 6 + 6x > 7 — 7x

[ -3x — x < -4
[ 6x + 7x > 7 — 6

[ -4x < -4
[ 13x > 1

[ x > 1
[ x > 1/13

x∈ (1/13, ∞)

ա) [ 3 (1 + x) — 2 < 5 (2 — 5x) — 3x
[ 2 (4 — x) — 3 > 4x — 7

[ 3 + 3x — 2 < 10 — 10x — 3x
[ 8 — 2x — 3 > 4x — 7

[ 3x + 10x + 3x < 10 — 3 + 2
[ -2x — 4x > -7 — 8 + 3

[ 16x < 9
[ -6x > -12

[ x < 9/16
[ x < 2

բ) [ 2 (3y — 1) — 1 ≥ 4 — 5y
[ 6y — 6 ≤ 6(y — 1)

[ 6y — 2 — 1 ≥ 4 — 5y
[ 6y — 6 ≤ 6y — 6

[ 6y + 5y ≥ 4 + 2 + 1
[ 6y — 6y ≤ -6 + 6

[ 11y ≥ 7
[ 0 = 0

գ) [ 3x + 3 > 3 (x + 1)
[ 2x — 2 < 2 (x — 1)

[ 3x + 3 > 3x + 3
[ 2x — 2 < 2x — 2

[ 3x — 3x > 3 — 3
[ 2x — 2x < -2 + 2

Լուծում չունի

դ) [ 4 — 4x ≥ 4 (1 — x)
[ 5x + 1 < 5x — 1

[ 4 — 4x ≥ 4 — 4x
[ 5x + 1 < 5x — 1

[ -4x + 4x ≥ 4 — 4
[ 5x — 5x < -1 — 1

Լուծում չունի

ե) [ 3 (2 — z) — 5z < -4 (27 — 3) + z
[ 6 (z — 3) ≥ 4z + 3

[ 6 — 3z — 5z < -108 + 12 + z
[ 6z — 18 ≥ 4z + 3

[ -3z — 5z — z < -108 + 12 + 6
[ 6z — 4z ≥ 3 + 18

[ -9z < -90
[ 2z ≥ 21

[ z > 10
[ z ≥ 21/2

զ) [ x ≤ x + 5
[ 4x — 3 > 3 — 4x

[ x — x ≤ 5
[ 4x + 4x > 3 + 3

[ 2x ≤ 5
[ 8x > 6

[ x ≤ 5/2
[ x > 6/8