For what values of x is \(\frac{x - 3}{4}\) + \(\frac{x + 1}{8}\) \(\geq\) 2 ?
A
x \(\geq\) 5
B
x \(\geq\) 6
C
x \(\geq\) 7
D
x \(\geq\) 8
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{x - 3}{4}\) + \(\frac{x + 1}{8}\) \(\geq\) 2
multiply through by the LCM of 4, 8, and 1 = 8
8(\(\frac{x - 3}{4}\)) + 8(\(\frac{x + 1}{8}\)) \(\geq\) 8 x 2
2(x - 3) + (x + 1) \(\geq\) 16
2x - 6 + x + 1 \(\geq\) 16
3x - 5 \(\geq\) 16
3x \(\geq\) 16 + 5 = 21
x \(\geq\) \(\frac{21}{3}\)
x \(\geq\) 7
Source: Myschool Past Questions Archive (Record #71823)