For what range of values of x is \(\frac{1}{2}\)x + \(\frac{1}{4}\) > \(\frac{1}{3}\)x + \(\frac{1}{2}\)?
A
x < \(\frac{3}{2}\)
B
x > \(\frac{3}{2}\)
C
x < -\(\frac{3}{2}\)
D
x > -\(\frac{3}{2}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{1}{2}\)x + \(\frac{1}{4}\) > \(\frac{1}{3}\)x + \(\frac{1}{2}\)
Multiply through by through by the LCM of 2, 3 and 4
12 x \(\frac{1}{2}\)x + 12 x \(\frac{1}{4}\) > 12 x \(\frac{1}{3}\)x + 12 x \(\frac{1}{2}\)
6x + 3 > 4x + 6
6x - 4x > 6 - 3
2x > 3
\(\frac{2x}{2}\) > \(\frac{3}{2}\)
x > \(\frac{3}{2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #29571)