12x-39greater than 9 and -4x+3< -6

Step-by-step explanation:

When you have an inequality like this, you can treat it like an equation except for one part.  If you ever divide or multiply it by a negative number or variable you have to flip the inequality.  if it is equal to as well you keep that though.  for instance

-5x ≤ 10

x ≥ -2

Anyway, in your case you have two inequalities, so you have to solve both and see what makes both true.

We'll start with 12x - 39 ≤ 9

12x - 39 ≤ 9 First add 39 to both sides

12x ≤ 48 Now divide both sides by 12, positive so no flipping

x ≤ 4

Next is:

-4x + 3 < -6 First subtract 3 from both sides

-4x < -9 Now divide both sides by -4, which means the sign flips

x > 9/4

Now, without even looking at the answers, what number or numbers are  less than or equal to 4 and greater than 9/4?  Well we pretty much described it there.  All numbers starting from, though not including 9/4, which is 2.25, all the way up to, and including 4.  B shows exactly that.

i believe the answer is the polygon, heptagon.