1) 18/a + 23 = 3/5
18/a = 3/5 - 23
18/a = 3/5 - 115/5
18/a = -112/5
a = 18 / (-112/5)
a = 18 * (-5/112)
a = -0.8036

2) 4/7 = 8 + 2a/21
2a/21 = 4/7 - 8
2a/21 = 4/7 - 56/7
2a/21 = -52/7
2a = 21 * (-52/7)
2a = -156
a = -78

3) 5/12 = 30/44 + 7a
5/12 - 30/44 = 7a
(55/132) - (60/132) = 7a
-5/132 = 7a
a = -5 / (7 * 132)
a = -5/924

4) 1/9 = 5a - 14/54
5a - 14/54 = 1/9
5a - 14/54 = 6/54
5a = 14/54 + 6/54
5a = 20/54
a = 20/54 / 5
a = 20/270
a = 2/27

5) 3/8 = 21 / (4(a+8))
3/8 = 21 / (4a + 32)
3/8 = 21 / 4(a + 8)
21 = 3(4(a + 8))
21 = 12(a + 8)
21 = 12a + 96
12a = -75
a = -75/12
a = -25/4

6) 14/45 = 7(a-5)/90
14/45 = 7(a-5)/90
14/45 = (7/90)(a-5)
14/45 = (1/13)(a-5)
14 = (1/13)(13)(a-5)
14 = a - 5
a = 14 + 5
a = 19