Simplify 6/7c - 5/9d - 1/2c + 1/3d.
A. 5/1c + 2/9d
B. 5/14c - 2/9d
C. 5/9c - 1/3d
D. 5/9c + 4/12 = 5/9c + 1/3d
To simplify the expression, you need to combine like terms. The like terms in the expression are the terms that have the same variable and exponent.
The expression 6/7c - 1/2c simplifies to (6/7 - 1/2)c. To find a common denominator for 7 and 2, you multiply them together: 7 * 2 = 14. So, the expression becomes (12/14 - 7/14)c, which simplifies to 5/14c.
Similarly, the expression -5/9d + 1/3d simplifies to (-5/9 + 3/3)d. To find a common denominator for 9 and 3, you multiply them together: 9 * 3 = 27. So, the expression becomes (-5/9 + 9/27)d, which simplifies to (1/9)d.
Therefore, the simplified expression is 5/14c + 1/9d.
The correct answer is B. 5/14c - 2/9d
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Expand 6 (x + 1)
To expand the expression 6(x + 1), you need to distribute the 6 to both terms inside the parentheses.
6(x + 1) = 6 * x + 6 * 1
Simplifying, we have:
6x + 6
Therefore, the expanded form of 6(x + 1) is 6x + 6.
Expand 4(3z - 7)
To expand the expression 4(3z - 7), you need to distribute the 4 to both terms inside the parentheses.
4(3z - 7) = 4 * 3z - 4 * 7
Simplifying, we have:
12z - 28
Therefore, the expanded form of 4(3z - 7) is 12z - 28.
Expand -5(2q + 8)
To expand the expression -5(2q + 8), you need to distribute the -5 to both terms inside the parentheses.
-5(2q + 8) = -5 * 2q - 5 * 8
Simplifying, we have:
-10q - 40
Therefore, the expanded form of -5(2q + 8) is -10q - 40.