a) 2/4 = 3/x
2 * x = 4 * 3
2x = 12
x = 12/2
x = 6
b) 4/12 = x/21
12 * x = 21 * 4
12x = 84
x = 84/12
x = 7
c) x/14 = 9/12
12 * x = 9 * 14
12x = 126
x = 126/12
x = 63/6
d) x/9 = 8/12
12 * x = 9 * 8
12x = 72
x = 72/12
e) 10 / 15 = 3x + 1 / 5x - 2
15 * (3x + 1) = 10 * (5x - 2)
45x + 15 = 50x - 20
50x - 45x = 15 + 20
5x = 35
x = 35/5
f) 8 / x + 1 = 12 / 2x - 6
8 * (2x - 6) = 12 * (x + 1)
16x - 48 = 12x + 12
16x - 12x = 12 + 48
4x = 60
x = 60/4
x = 15
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a) 2/4 = 3/x
2 * x = 4 * 3
2x = 12
x = 12/2
x = 6
b) 4/12 = x/21
12 * x = 21 * 4
12x = 84
x = 84/12
x = 7
c) x/14 = 9/12
12 * x = 9 * 14
12x = 126
x = 126/12
x = 63/6
d) x/9 = 8/12
12 * x = 9 * 8
12x = 72
x = 72/12
x = 6
e) 10 / 15 = 3x + 1 / 5x - 2
15 * (3x + 1) = 10 * (5x - 2)
45x + 15 = 50x - 20
50x - 45x = 15 + 20
5x = 35
x = 35/5
x = 7
f) 8 / x + 1 = 12 / 2x - 6
8 * (2x - 6) = 12 * (x + 1)
16x - 48 = 12x + 12
16x - 12x = 12 + 48
4x = 60
x = 60/4
x = 15