DESIGUALDADES SIMPLES LINEALES BANCO DE EJERCICIOS

BANCO DE EJERCICIOS

DESIGUALDADES SIMPLES LINEALES

1) 3x – 7 < 3 – 2 [ 0,5 ]

3x – 7 + 7 < 3x – 2 + 7

3x < 3x + 5

3x - 3x < 3x + 5 - 3x

0 < 5

3(5) - 7 < 3 (5) - 2 0 5

15 - 7 < 15 - 2

8 < 13

3 (0) - 7 < 3 (0) - 2

0 - 7 < 0 - 2

-7 < -2

2) 3x + 5 ≤ - 7x + 8 ( -∞, 3/10]

3x + 5 - 5 ≤ - 7x + 8 - 5

3x ≤ - 7x + 3

3x + 7x ≤ - 7x + 3 + 7x

10x ≤ 3 -∞

X ≤ 3/10

3(0) + 5 ≤ - 7(0) + 8 0 3/10

5 ≤ 8

3 (3/10) + 5 ≤ 7 (3/10) + 8

9/10 + 5 ≤ - 21/10 + 8

59/10 ≤ 59/10

3) 2 + x < 9x + 6 ( - 1/2 , + ∞ )

2 - 2 + x < 9x + 6 - 2

X < 9x + 4

X - 9x < 9x + 4 - 9 x

-8 x < 4

X = -4/8 ½ 0

X = -1/2

2 + (0) < 9 (0) + 6

2 < 6

2 - 1/2 < 9 (-1/2) + 6

3/2 < 9/2 + 6

3/2 < 3/2

DESIGUALDADES DOBLES

1) - 3 ≤ 6x - 1 < 3 [-1/3, 2/3)

-3 + 1 ≤ 6x -1 + 1 < 3 + 1

-2 ≤ 6x < 4

-2 (1/2) ≤ 6x (1/6) < 4 (1/6)

-2/6 ≤ x < 4/6

-1/3 ≤ x < 2/3

-3 ≤ 6(0) - 1 < 3 1/3 0 2/3

-3 ≤ - 1 < 3

-3 ≤ 6 (-1/3) < 3

-3 ≤ -6/3 < 3

-3≤ - 2 < 3

-3≤ 6 (2/3) < 3

-3 ≤ 12/3 < 3

-3 ≤ 4 < 3

2) -1 ≤ 2 - 3x ≤ 11 [-1, 3)

-1 - 2 ≤ 2 - 3 x - 2 ≤ 11 - 2

-3 ≤ 3x ≤ 9

-3 (1/3) ≤ 3x (1/3) ≤ 9 (1/3)

-1/3 ≤ x ≤ 9/3

-1 ≤ x ≤ 3

-1 ≤ 2 - 3 (0) ≤ 11 -1 0 3

-1 ≤ 2 ≤ 11

-1 ≤ 2 - 3 (-1) ≤ 11

-1 ≤ 3 ≤ 11

- 1≤ 2 - 3 (3) ≤ 11

-1 ≤ - 7 ≤ 11

3) 2/3x - 2 < 2x - 3 < 6 + 2/3x ( 3/4, 27/4)

2/3x - 2 - 2/3x < 2x - 3 < 6 + 2/3x

-2 < 4/3 x - 3 < 6

-2 + 3 < 4/3x - 3 + 3 < 6 + 3

1 < 4/3x - 3 + 3 < 6 + 3

1 (3/4) < 4/3x (3/4) < 9 (3/4)

3/4 < x <

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