Question

Which is the simplified form of the expression 3(7/5x+4) - 2(3/2 - 5/4x)?

A. -39/5x - 11/2
B. 67/10x + 9
C. 3/10x + 5/2
D. 15 + 76/10x

Answer 1

B. 67/10x + 9

Explanation:

Answer 2

B.
`(67)/(10) x + 9`

Explanation:

Simplify the expression. Remember to go by the order of operations, or PEMDAS.

1) First, distribute the numbers outside of the set of parentheses to the terms inside the set of parentheses next to them. Then, simplify the fractions.

`3((7)/(5) x + 4) -2 ((3)/(2) -(5)/(4) x)`

`(21)/(5)x + 12 - (6)/(2) + (10)/(4) x`

`(21)/(5) x + 12 - 3 + (10)/(4) x`

2) Finally, combine like terms. (This means to add or subtract constants and to add or subtract terms with the same variables.) You may need to convert terms to the same denominator in order to do so easier. Then, reduce the fraction.

`(21)/(5) x + 9 + (10)/(4)x \\(84)/(20)x + (50)/(20)x + 9 \\(134)/(20)x + 9 \\(67)/(10)x + 9`

Thus, the answer is
`(67)/(10) x + 9`.