Question

A) 32
---- Este subunitara
2x+4


B) 2x+3
-------- Este supraunitară
3x-5

Answer 1

32/(2x + 4) = subunitara =>

32 < 2x + 4

28 < 2x

x > 14

(2x + 3)/(3x - 5) = supraunitara =>

2x + 3 > 3x - 5

2x - 3x > -3 - 5

-x > -8

x < 8

Answer 2

a)

32

---------- → fractie subunitara ( numaratorul < numitorul )

2 x + 4

2 x + 4 > 32 ⇒ 2 x > 32 - 4 ⇒ 2 x > 28 ⇒ x > 28 : 2 ⇒ x > 14

⇒valorile lui x sunt: [ 15, 16 , 17, .........+ ∞)

2 x + 4 = 2× 15 + 4 = 34 > 32

2 x + 4 = 2×16 + 4 = 36 > 32

32 / 34; 32 / 36 ; 32 / 36 ; 32 / 38; 32 / 40; 32 / 42 → fractii subunitare

b)

2 x + 3

______ → fractie supraunitara ( numaratorul > numitorul )

3 x - 5

3 x - 5 < 2 x + 3

3 x - 2 x < 3 + 5

x < 8 ⇒ 3 x > 5 ⇒ x = ( 2; 3; 4; 5; 6; 7 ) ∈ N ( pentru inv. primar)

2 x + 3 2 ×2 + 3 7

---------; -------------- = ------ → fractie supraunitara 7 > 1

3 x - 5 3 ×2 - 5 1

( 2 × 3 + 3 ) / ( 3 × 3 - 5) = 9 / 4 ; / = linie de fractie

( 2 × 4 + 3) / ( 3 × 4 - 5 ) = 11 / 7 → fractie supraunitara

( 2 × 5 + 3) / ( 3 × 5 - 5 ) = 13 / 10

( 2 × 6 + 3 ) / ( 3× 6 - 5 ) = 15 / 13

( 2 × 7 + 3 ) / ( 3 × 7 - 5 ) = 17 / 16 → fractie supraunitara