\(\frac{x - 3}{4}\) + \(\frac{x + 1}{8}\) \(\geq\) 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