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:

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

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step-by-step explanation: