SOLVING INEQUALITIES BY CLEARING THE FRACTIONS

Problem 2 :

(7/13)x  - 1 > 1/2

Solution :

Add 1 to both sides

(7/13)x  - 1 + 1 > (1/2) + 1

(7/13)x > 3/2

Multiply both sides by 13/7

(7/13)x (13/7) > (3/2) (13/7)

x > 39/14

Converting improper fraction into mixed fraction, we get

x > 2 11/14

Problem 3 :

(4/5) ≥ (2/3) - (2/7x)

Solution :

(4/5) ≥ (-2/7x) + (2/3)

Subtract 2/3 from both sides.

(4/5) - 2/3 ≥ (-2/7x) + 2/3 - 2/3

2/15 ≥ (-2/7)x

Since we multiply both sides by (-7/2), change inequality ≥ into ≤

(2/15) (-7/2) ≥ (-2/7)x (-7/2)

-7/15 ≤ x

Problem 4 :

(8/15x) – (17/30) < 7/10

Solution :

Add 17/30 to both sides

(8/15x) – (17/30) + 17/30 < (7/10) + 17/30

8/15x < 38/30

Multiply both sides by 15/8

(8/15)x (15/8) < (38/30) (15/8)

x < 19/8

Problem 5 :

(-4/11)z - 1 > (-8/11)

Solution :

Add 1 to both sides

(-4/11)z – 1 + 1 > (-8/11) + 1

(-4/11)z > 3/11

Since we multiply both sides by (-11/4), change inequality > into <

(-4/11)z (-11/4) > (3/11) (-11/4)

z < -3/4

Problem 6 :

(1/5k) + 14 ≤ 2/9

Solution :

Subtract 14 from both sides

(1/5k) + 14 – 14 ≤ 2/9 – 14

1/5k ≤ -124/9

Multiply both sides by 5

(1/5)k (5) ≤ (-124/9) (5)

k ≤ -620/9

Converting improper fraction into mixed fraction, we get

k ≤ -68  8/9

Problem 7 :

-31/4 < -13 + (7/8f)

Solution :

-31/4 < -13 + (7/8f)

Add 13 to both sides

-31/4 +13 < -13 + 13 + (7/8)f 

21/4 < 7/8f 

Multiply both sides by 8/7

(21/4) (8/7) < (7/8f) (8/7) 

6 < f

Problem 8 :

(1/7r) + (53/56) > 6/7

Solution :

Subtract 53/56 from both sides

(1/7)r + (53/56) – (53/56) > (6/7) – (53/56)

1/7r > -5/56

Multiply both sides by 7

(1/7)r (7) > (-5/56) (7)

r > -5/8

Problem 9 :

(5/6n) – (1/5) < -8/15

Solution :

Add 1/5 to both sides

(5/6)n – (1/5) + (1/5) < (-8/15) + (1/5)

5/6n < -5/15

Multiply both sides by 6/5

(5/6n) (6/5) < (-5/15) (6/5)

n < -2/5

Problem 10 :

(1/3) + (1/13d) ≥ 17/39

Solution :

Subtract 1/3 from both sides

(1/3) - (1/3) + (1/13)d ≥ (17/39) - (1/3)

1/13d ≥ 14/39

Multiply both sides by 13

(1/13d) (13) ≥ (14/39) (13)

d ≥ 14/13

d ≥ 1 1/13