Select all of the expressions that are equivalent to 1/3(−5x−6/2)−7/8 .
A.−20x−45/24
B.−5x−6/6−7/8
C.−8x/24+21/24
D.5x−6−21/12
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To determine the expressions that are equivalent to 1/3(-5x - 6/2) - 7/8, we can simplify each expression and compare them to the original.
1. Start by simplifying the expression within the parentheses: -5x - 6/2 becomes -5x - 3.
2. Now, distribute 1/3 to the simplified expression: (1/3)(-5x - 3) = (-5/3)x - 1.
3. Next, subtract 7/8 from the result: (-5/3)x - 1 - 7/8.
4. To combine the fractions, find a common denominator. In this case, it is 24. Multiply -1 by 8/8 and -7/8 by 3/3: (-5/3)x - 8/8 - 21/24.
5. Now the expression becomes: (-5/3)x - 29/24.
Comparing this simplified expression to the given options:
A. -20x - 45/24:
To check if it is equivalent, simplify the expression: -20x - 45/24 = (-20/1)x - 45/24 = -20x - 45/24.
B. -5x - 6/6 - 7/8:
Simplify the expression: -5x - 6/6 - 7/8 = -5x - 1 - 7/8 = -5x - 8/8 - 7/8 = -5x - 15/8.
C. -8x/24 + 21/24:
Simplify the expression: -8x/24 + 21/24 = (-8x + 21)/24.
D. 5x - 6 - 21/12:
Simplify the expression: 5x - 6 - 21/12 = 5x - 6 - 7/4 = 5x - 8/4 - 7/4 = 5x - 15/4.
Therefore, the expressions that are equivalent to 1/3(-5x - 6/2) - 7/8 are A. -20x - 45/24 and C. -8x/24 + 21/24.