To make x the subject of the given equations:
1. y = x/(x-7)
Multiplying both sides by (x-7), we get:
y(x-7) = x
Rearranging, we get:
x - y(x-7) = 0
x - yx + 7y = 0
x(1-y) = -7y
x = -7y/(y-1)
2. y = (x+2)/(x-5)
Multiplying both sides by (x-5), we get:
y(x-5) = x+2
Rearranging, we get:
x - y(x-5) = 2
x - yx + 5y = 2
x(1-y) = 2 - 5y
x = (2-5y)/(1-y)
3. y = (a-2x)/(bx+8)
Multiplying both sides by (bx+8), we get:
y(bx+8) = a-2x
Rearranging, we get:
2x = a - ybx - 8y
x = (a - ybx - 8y)/2
4. y = (5x-12)/(5x-7)
Multiplying both sides by (5x-7), we get:
y(5x-7) = 5x-12
Rearranging, we get:
5xy - 7y = 5x - 12
5x(y-1) = 7y - 12
x = (7y-12)/(5y-7)
5. w/8 + 9/x = 2
Multiplying both sides by 8x, we get:
wx + 72 = 16x
Rearranging, we get:
wx - 16x = -72
x(w-16) = -72
x = -72/(w-16)