Simplify 1/4y + 1 1/2 + 2 - 1 3/4y - 12

(-1 (3 y + 17)) / 2

Step-by-step explanation:

Simplify the following:

y/4 - (1 + 3/4) y - 12 + 1/2 + 1 + 2

Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:

y/4 - 4/4 + 3/4 y - 12 + 1/2 + 1 + 2

4/4 + 3/4 = (4 + 3) / 4:

y/4 - (4 + 3) / 4 y - 12 + 1/2 + 1 + 2

4 + 3 = 7:

y/4 - 7 y/4 - 12 + 1/2 + 1 + 2

Put each term in y/4 - (7 y) / 4 - 12 + 1/2 + 1 + 2 over the common denominator 4: y/4 - (7 y) / 4 - 12 + 1/2 + 1 + 2 = y/4 - (7 y) / 4 - 48/4 + 2/4 + 4/4 + 8/4:

y/4 - (7 y) / 4 - 48/4 + 2/4 + 4/4 + 8/4

y/4 - (7 y) / 4 - 48/4 + 2/4 + 4/4 + 8/4 = (y - 7 y - 48 + 2 + 4 + 8) / 4:

(y - 7 y - 48 + 2 + 4 + 8) / 4

Grouping like terms, y - 7 y - 48 + 2 + 4 + 8 = (y - 7 y) + (4 + 2 + 8 - 48):

((y - 7 y) + (4 + 2 + 8 - 48)) / 4

y - 7 y = - 6 y:

(-6 y + (4 + 2 + 8 - 48)) / 4

4 + 2 + 8 - 48 = - 34:

(-34 - 6 y) / 4

Factor - 2 out of - 6 y - 34:

(-2 (3 y + 17)) / 4

The gcd of - 2 and 4 is 2, so (-2 (3 y + 17)) / 4 = ((2 (-1)) (3 y + 17)) / (2*2) = 2/2 * ( - (3 y + 17)) / 2 = ( - (3 y + 17)) / 2:

Answer: (-1 (3 y + 17)) / 2