To solve the equation sin(3x+10) = -1/2, we can use the inverse sine function (also known as arcsin or sin^(-1)) to find the values of (3x+10) that give a sine of -1/2.

The inverse sine of -1/2 is -π/6 or -30 degrees. So, we have:

3x + 10 = -π/6 + 2πn or 3x + 10 = -30° + 360°n

where n is an integer representing the number of complete cycles.

Now, let's solve for x:

3x = -π/6 - 10 + 2πn or 3x = -30° - 10 + 360°n

Divide both sides by 3:

x = (-π/6 - 10 + 2πn) / 3 or x = (-30° - 10 + 360°n) / 3

Simplifying further:

x = (-π/18 - 10/3 + 2πn/3) or x = (-40°/3 + 120°n/3)

Therefore, the solutions for the equation sin(3x+10) = -1/2 are:

x = (-π/18 - 10/3 + 2πn/3) or x = (-40°/3 + 120°n/3)

where n is an integer.