Answer:
The simplified expression is -13/12. (are you sure you don't have a typo somewhere), double checked.
Explanation:
First, let's simplify the expression inside the absolute value bars:
5/6 - 17/12 = 10/12 - 17/12 = -7/12
Next, we can simplify the expression outside the absolute value bars:
| -7/12 | - | 5/3 |
= 7/12 - 5/3 (since the absolute value of -7/12 is 7/12)
= 7/12 - 20/12
= -13/12
The simplified expression is -13/12.
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Simplify the following:
abs(5/6 - 17/12) - abs(5/3)
Put 5/6 - 17/12 over the common denominator 12. 5/6 - 17/12 = (2×5)/12 - 17/12:
abs(((2×5)/12 - 17/12)) - abs(5/3)
2×5 = 10:
abs(10/12 - 17/12) - abs(5/3)
10/12 - 17/12 = (10 - 17)/12:
abs(((10 - 17)/12)) - abs(5/3)
10 - 17 = -7:
abs((-7)/12) - abs(5/3)
Since 5/3 is a non-negative constant, abs(5/3) = 5/3:
abs(-7/12) - 5/3
Since -7/12 is a negative constant, abs(-7/12) = 7/12:
7/12 - 5/3
Put 7/12 - 5/3 over the common denominator 12. 7/12 - 5/3 = 7/12 + (4 (-5))/12:
7/12 - (5×4)/12
4 (-5) = -20:
7/12 + (-20)/12
7/12 - 20/12 = (7 - 20)/12:
(7 - 20)/12
7 - 20 = -13:
Answer: (-13)/12