2 4/7 : (0,5х - 23/35 ) = 7,5
0,5х - 23/35 = 2 4/7 : 7,5
0,5х - 23/35 = 18/7 * 10/75
0,5х - 23/35 = 18/7 * 2/15
0,5х = 12/35 + 23/35
0,5 х = 1
х = 1 / 0,5 = 10/5
х= 2
проверим:
2 4/7 : ( 0,5 * 2 - 23/35) = 7,5
(18/7) : ( 1 - 23/35) =7,5
(18/7) : (12/35) = 7,5
18/7 * 35/12 =7,5
(3*5)/(2*1) = 7,5
15/2 = 7,5
7,5=7,5
2) ( 1 2/7 * у - 1/2 ) : 2,5 =5,2
1 2/7 * у - 0,5 = 5,2 * 2,5
1 2/7 *у = 13 +0,5
у = 13,5 : 1 2/7 = 27/2 * 7/9= (3*7) /(2*1)=21/2
у= 10,5
проверим:
(1 2/7 * 10,5 - 1/2) : 2,5 = 5,2
(9/7 * 21/2 - 1/2 ) : 2,5 = 5,2
(27/2 - 1/2) : 2,5 = 5,2
13 : 2,5 = 5,2
5,2=5,2
3)(1/4 + 3/4 * х ) : 0,45 = 25/36
1/4 + 3/4 * х = 25/36 * 45/100
1/4 + 3/4 * х = 25/36 * 9/20
1/4 + 3/4 * х = (5 * 1) / (4*4)
1/4 + 3/4 * х = 5/16
3/4 * х= 5/16 - 1/4
3/4 * х = 5/16 - 4/16
3/4 * х = 1/16
х = 1/16 : 3/4 = 1/16 * 4/3 = 1/12
х = 1/12
проверим:
( 1/4 + 3/4 * 1/12 ) : 0,45 =25/36
(1/4 + 1/16) : (45/100) = 25/36
5/16 * (100/45) = 25/36
5/16 * (20/9) = 25/36
(5*5)/(4*9) = 25/36
25/36 = 25/36
4) 22 * (17/26 * х - 3/4) = 5 1/13
17/26 * х - 3/4 = 66/13 : (22/1)
17/26 * х - 3/4 = 66/13 * 1/22
17/26 * х - 3/4 = 3/13
17/26 * х = 3/13 + 3/4
17/26 * х = 12/52 + 39/52
17/26 * х = 51/52
х = 51/52 : 17/26 = 51/52 * 26/17 = (3*1)/(2*1)= 3/2
х = 1,5
проверим:
22 * (17/26 * 1,5 - 3/4) = 5 1/13
22 * ( 17/26 * 3/2 - 3/4) = 5 1/13
22 * ( 51/52 - 39/52) = 5 1/13
22/1 * 12/52 = 5 1/13
22/1 * 3/13 = 5 1/13
66/13 = 5 1/13
5 1/13 = 5 1/13