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1 3/4 + 1/6 + x = 7 1/2
 
Always put the + sign into mixed numbers:
 
1 + 3/4 + 1/6 + x = 7 + 1/2
 
A. Method 1: Fraction Manipulation
 
Subtract 1 + 3/4 + 1/6 from both sides:
 
x = 7 + 1/2 – 1 – 3/4 – 1/6
 
x = 7 + 1/2 – 2/2 – 3/4 – 1/6
 
x = 7 – 1/2 – 3/4 – 1/6
 
x = 7 – 2/4 – 3/4 – 1/6
 
x = 7 – 5/(2*2) – 1/(2*3)
 
x = 7 – (5*3/(2*2*3) + 2*1/(2*2*3))
 
x = 7 – (5*3 + 2*1)/(2*2*3)
 
x = 7 – 17/12 = 7 – (12+5)/12
 
x = 7 – 1 – 5/12 = 6 – 5/12
 
x = 5 + 12/12 – 5/12 = 5 + 7/12
 
B. Method 2: Clear Fractions First
 
1 + 3/4 + 1/6 + x = 7 + 1/2
 
Multiply both sides by 2*2*3:
 
2*2*3*1 + 2*2*3*3/4 + 2*2*3*1/6 + 2*2*3*x = 2*2*3*7 + 2*2*3*1/2
 
12 + 9 + 2 + 12x = 84 + 6
 
23 + 12x = 90
 
12x = 90 – 23 = 67
 
x = 67/12 = (60 + 7)/12
 
x = 5 + 7/12
 
For this question it is best to find the least common denominator (LCD) for all terms. In this case that denominator is 12.
Using the LCD you would convert all of the fractions into the following equation and solve:
1 9/12 + 2/16 + __ = 7 6/12
1 11/12 + __ = 7 6/12
___ = 7 6/12 - 1 11/12
___ = 5 7/12