Question

Which of the following choices is a solution for the inequality:

A: 51/28
B: 51/29
C: 7/4
D: 3/2

Answer 1

B

Explanation:

given

`(2x+9)/(3)` +
`(7x+3)/(4)` > 8

multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions

12 ×
`(2x+9)/(3)` + 12 ×
`(7x+3)/(4)` > 12 × 8 ( simplify both sides )

4(2x + 9) + 3(7x + 3) > 96 ← distribute parenthesis on left side and simplify

8x + 36 + 21x + 9 > 96

29x + 45 > 96 ( subtract 45 from both sides )

29x > 51 ( divide both sides by 29 )

`(29)/(29)` x >
`(51)/(29)` , that is

x >
`(51)/(29)`