a) To solve the equation 3 + x = -8, we need to isolate the variable x.

First, we can subtract 3 from both sides of the equation:

3 + x - 3 = -8 - 3

This simplifies to:

x = -11

So the solution to the equation is x = -11.

b) To solve the equation (35 + x) - 12 = 27, we need to isolate the variable x.

First, we can simplify the equation by combining like terms:

35 + x - 12 = 27

This simplifies to:

23 + x = 27

Next, we can subtract 23 from both sides of the equation:

23 + x - 23 = 27 - 23

This simplifies to:

x = 4

So the solution to the equation is x = 4.

c) To solve the equation 2^x + 15 = 31, we need to isolate the variable x.

First, we can subtract 15 from both sides of the equation:

2^x + 15 - 15 = 31 - 15

This simplifies to:

2^x = 16

Next, we can take the logarithm of both sides of the equation to solve for x:

log(2^x) = log(16)

Using the logarithmic property log(a^b) = b*log(a), we can rewrite the equation as:

x*log(2) = log(16)

Finally, we can divide both sides of the equation by log(2) to solve for x:

x = log(16) / log(2)

Using a calculator, we find that x ≈ 4.

So the solution to the equation is x ≈ 4.