Start: 3(x+1) + (5x+3)/2 = -2

Expand brackets: 3x+3 + (5/2)x + 3/2 = -2

Multiply both sides by 2 (makes it easier not to have the fractions): 6x+6 + 5x + 3 = -4

Combine the x's: 11x+6 + 3 = -4

Combine 6 and 3: 11x+9 = -4

Subtract 9 from both sides: 11x+9-9 = -4-9

Simplify: 11x = -13

Divide both sides by 11: 11x/11 = -13/11

Simplify: x = -13/11

Now, let me check ...

3(-13/11 +1) + (5 * (-13/11)+3)/2 = -2

3(-2/11) + (-65/11 + 33/11)/2 = -2

-6/11 + (-32/11)/2 = -2

-6/11 - 16/11 = -2

-22/11 = -2

-2 = -2

YAY!