Option: A is the correct answer.
A. x+6 ≥ 2 and 2x-3 ≤ 9
From the graph that is provided to us we see that the solution set is:
x ≥ -4 and x ≤ 6
using the first equality we have:
x ≥ -4
on adding 6 on both side of the inequality we have:
x+6 ≥ -4+6
i.e. x+6 ≥ 2
and using the second inequality we have:
x ≤ 6
i.e. on multiplying both side of the inequality by 2 we get:
2x ≤ 12
Now on subtracting both side by 3 we get:
2x-3 ≤ 12-3
⇒ 2x-3 ≤ 9
Hence, the compound inequality that graph be the solution of is:
x+6 ≥ 2 and 2x-3 ≤ 9
