1) Simplifying the equation 3z - 14/2 = -1:
3z - 7 = -13z = 6z = 2
2) Simplifying the equation 3n + 75/5 = 6n + 42/5:
3n + 15 = 6n + 815 = 3n + 87 = 3nn = 7/3
3) Simplifying the equation 4/x - x + 8/2x = 5/6:
4/x - x + 4/x = 5/6(4 + x^2 + 8) / x = 5/6(x^2 + 12) / x = 5/66(x^2 + 12) = 5x6x^2 + 72 = 5x6x^2 - 5x + 72 = 0
Solving this quadratic equation for x would provide the value(s) that satisfy the equation.
1) Simplifying the equation 3z - 14/2 = -1:
3z - 7 = -1
3z = 6
z = 2
2) Simplifying the equation 3n + 75/5 = 6n + 42/5:
3n + 15 = 6n + 8
15 = 3n + 8
7 = 3n
n = 7/3
3) Simplifying the equation 4/x - x + 8/2x = 5/6:
4/x - x + 4/x = 5/6
(4 + x^2 + 8) / x = 5/6
(x^2 + 12) / x = 5/6
6(x^2 + 12) = 5x
6x^2 + 72 = 5x
6x^2 - 5x + 72 = 0
Solving this quadratic equation for x would provide the value(s) that satisfy the equation.