1/2x+3/2(x+1)-1/4=5 (Expand the polynomial)
(1/2x+3/2x)+3/2-(1/4)=5
4/2x+3/2-(1/4)=5
4/2x+(3/2–1/4)-(3/2–1/4)=5-(3/2–1/4)
4/2x+0=5-(3/2–1/4) (Express the fractions on the right side of the equation in the common denominator 4)
2x=5-(6/4–1/4)
2x=5-(5/4)
2x=3 3/4
2x/2=(3 3/4)/2
x=15/4(1/2)
x=
15/8 or 1 7/8 as a mixed fraction or 1.875 as a decimal numeral
PROOF
If x=15/8, then the inverse of the equation 1/2x+3/2(x+1)-1/4=5 returns
2x+(6/4–1/4)=5
2(15/8)+(6/4–1/4)=5
15/4+(5/4)=5
(15+5)/4=5
20/4=5 and
5=5 proves the root (zero) x=15/8 of the statement 1/2x+3/2(x+1)-1/4=5
C.H.
1/2x+3/2(x+1) --1/4=5
1/2 (1/x+3/ (x+1) =5+1/4
1/x + 3/x+1 =(5+1/4) ×2/1
x+ 1 +3x /x (x+1) = 10+1/2 =21/2
4x+1 = 21/2 [x^2+x]
8x+2= 21x^2+21x
21x^2 +-13 x -2 =0
a =21 b= 13 c= -2
X= [13 + -- (169 -- 4×21× -2)^1/2 ] /2×21
=[13 + - ( 169 + 168 )^1/2] /2×21
Discriminat =169+168=337 >0