2/3 (18x - 9/10) + 7/2 (8x + 1)
Responses:
40x + 1/10
40x + 16/5
40x - 19/5
40x - 1/2
To simplify the expression, we can distribute the coefficients onto the terms inside the parentheses and then combine like terms.
First, let's apply the coefficient of 2/3 to the terms inside the first set of parentheses:
(2/3)(18x - 9/10) = (36/3)x - (18/3)(9/10) = 12x - 27/10
Next, let's apply the coefficient of 7/2 to the terms inside the second set of parentheses:
(7/2)(8x + 1) = (56/2)x + (7/2)(1) = 28x + 7/2
Now, let's combine the two simplified terms:
12x - 27/10 + 28x + 7/2
To add fractions, we need a common denominator. The least common denominator (LCD) of 10 and 2 is 10, so we'll convert the fractions:
12x - (27/10)(2/2) + 28x + (7/2)(5/5)
12x - 54/20 + 28x + 35/10
Now, let's combine the like terms:
(12x + 28x) + (-54/20 + 35/10)
40x + (-54/20 + 70/20)
40x + 16/20
Simplifying the fraction:
40x + 4/5
So, the simplified expression is 40x + 4/5.