Translate the following word problems into algebraic equations. The variable 'x' should represent the unknown number.

Step 1: Write the equation for each statement.

a) The sum of a number and 3 is 10.
Let the number be $x$.

$$x + 3 = 10$$

b) 12 subtracted from a number is 23.
Let the number be $x$.

$$x - 12 = 23$$

c) 5 times a number is 75.
Let the number be $x$.

$$5x = 75$$

d) One-sixth of a number is -6.
Let the number be $x$.

$$\frac{x}{6} = -6$$

e) 16 added to three times a number is 1.
Let the number be $x$.

$$3x + 16 = 1$$

f) 5 times a number subtracted from 2 is 12.
Let the number be $x$.

$$2 - 5x = 12$$

g) If you take away 7 from 2 times a number, you get 11.
Let the number be $x$.

$$2x - 7 = 11$$

h) If 3 is added to one-third of a number, you get 6.
Let the number be $x$.

$$\frac{x}{3} + 3 = 6$$

Here are the equations:

*a) $\boxed{x + 3 = 10}$

*b) $\boxed{x - 12 = 23}$

*c) $\boxed{5x = 75}$

*d) $\boxed{\frac{x}{6} = -6}$

*e) $\boxed{3x + 16 = 1}$

*f) $\boxed{2 - 5x = 12}$

*g) $\boxed{2x - 7 = 11}$

*h) $\boxed{\frac{x}{3} + 3 = 6}$