Let x represent that number
Translate this “If twice a number added to 3 is divided by the number plus 1, the result is three halves into an equation" which is:
2x+3/x+1=3/2
Times x+1 to each side
(2x+3/x+1)(x+1)=3/2(x+1)
2x+3=3/2x+3/2
2x+3=1.5x+1.5
Subtract 1.5x to each side
2x+3-1.5x=1.5x+1.5-1.5x
0.5x+3=1.5
Subtract 3 to each side
0.5x+3-3=1.5-3
0.5x=-1.5
Divided 0.5 to each side
0.5x/0.5=-1.5/0.5
x=-3
Check:
2x+3/x+1=3/2
2(-3)+3/-3+1=3/2
-6+3/-2=3/2
-3/-2=3/2
3/2=3/2. As a result, the number is -3. Hope it help!