Help with this algebra 2 question?

(1/2)a - 5 ≥ -3              or   -6a - 14 ≤ -56
(1/2)a - 5 + 5 ≥ -3 + 5  or  -6a - 14 + 14 ≤ -56 + 14
(1/2)a ≥ 2                     or   -6a ≤ -42
(1/2)a × 2 ≥ 2 × 2         or   -6a × (-1/6) ≥ -42 × (-1/6)
a ≥ 4                             or   a ≥ 7
Hence, a ≥ 4

Option A represents "a ≤ 4 or a ≥ 7"
Option B represents "a ≥ 4"
Option C represents "a ≥ 7"
Option D represent "4 ≤ a ≤ 7"

The answer: B.

(1/2)a - 5 ≥ -3
(1/2)a ≥ 2
a ≥ 4 ..................(1)

-6a - 14 ≤ -56
42 ≤ 6a
a ≥ 7 ..................(2)

Answer is a ≥ 4, (which includes a ≥ 7)
Number line image that matches is B

There's a tie, so let's see if I can break it.

The problem with turning it into an equation is you could lose the direction of the signs.  So let's not do that and keep them as inequalities:

(1/2)a - 5 ≥ -3 or -6a - 14 ≤ -56

Let's add 5 to both sides in the first one and 14 in the second:

(1/2)a ≥ 2 or -6a ≤ -42

Multiply both sides by 2 in the first and divide by -6 in the second.  This requires that you flip the sign:

a ≥ 4 or a ≥ 7

So now both point the same direction.  So anything that is true in the second will also be true in the first.

Since you want them "OR"ed, (vs. "AND"ed)

So the answer is B:  a ≥ 4

Graph represented by B