Question

25 POINTS for this question. Find all the integer solutions to each system of the inequalities:

Answer 1

Answer:

The integer solutions are  4,5,6 and 7.

Step-by-step explanation:

12a - 37 > 0

12a > 37

a > 37/12

a > 3 .083.

6a ≤ 42

a ≤ 7.

Answer 2

Answer:

Step-by-step explanation:

12a-37 > 0  ...(1)

6a ≤ 42....(2)

by (1) : a ≤ 7   but  a  is the integer number so : a =1  ; a =2 : a =3  : a=4 ; a = 5

 a = 6 and a = 7

1) cas : a = 1   by (2) : 12(1) -37 > 0   -25 > 0 ...... false

2) cas : a = 2   by (2) : 12(2) -37 > 0   -13 > 0 ...... false

3) cas : a = 3   by (2) : 12(3) -37 > 0   -1 > 0 ...... false

4) cas : a = 4   by (2) : 12(4) -37 > 0   11 > 0 ...... true

5) cas : a = 5   by (2) : 12(5) -37 > 0  23> 0 ...... true

6) cas : a =6   by (2) : 12(6) -37 > 0   35 > 0 ...... true

7) cas : a = 7  by (2) : 12(7) -37 > 0   47 > 0 ...... true

all the integer solutions to each system of the inequalities: 4 ; 5; 6: 7 .