Find all real numbers which satisfy the inequality \(\frac{3}{5}\)x + 3 > \(\frac{2}{3}\)x - 4
A
x > 105
B
x > 7
C
x < 7
D
x < 105
Verified Correct Answer: .
Step-by-Step Mathematical Solution
\(\frac{3}{5}\)x + 3 > \(\frac{2}{3}\)x - 4
Multiply through by the LCM of 5 and 3, which are the denominators of the two fractions.
15 X \(\frac{3}{5}\)x + (3 X 15) > 15 X \(\frac{2}{3}\)x - (4 X 15)
3 X 3x + 45 > 5 X 2x - 60
9x + 45 > 10x - 60
Collect like terms
9x - 10x > -60 - 45
- x > - 105
Divide through by -1
\(\frac{- x}{ - 1}\) > \(\frac{-105}{-1}\)
x < 105
Source: Myschool Past Questions Archive (Record #78164)