Solve: - \(\frac{1}{4}\) < \(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\)
A
-\(\frac{5}{9}\) < x <\(\frac{8}{9}\)
B
-\(\frac{8}{9}\) < x <\(\frac{7}{9}\)
C
-\(\frac{8}{9}\) < x <\(\frac{5}{9}\)
D
-\(\frac{7}{9}\) < x <\(\frac{8}{9}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\); \(\frac{3}{4}\) (3x - 2) > - \(\frac{1}{4}\)
3(3x - 2) < 2; 3(3x - 2) > -1
9x - 6 < 2; 9x - 6 > -1
9x < 8; 9x > 5
x < \(\frac{5}{9}\); x > \(\frac{8}{9}\)
Source: Myschool Past Questions Archive (Record #49984)