Answer:
The system of inequalities 45 > 4x + 9 and 53 ≤ 4x + 9 doesn't have any solution, because the restrictions on x are contradictory (x can't be both less than 9 and greater than or equal to 11).
Explanation:
These are a set of compound inequalities. Let's solve these equations step by step. The first inequality 45 > 4x + 9, we start to solve it by subtracting 9 from both sides of the inequality, which gives us 36 > 4x. Then, we divide each side by 4 to get x < 9.
The second inequality is 53 ≤ 4x + 9. We solve this by subtracting 9 from both sides to get 44 ≤ 4x. Then, we divide each side by 4 to find x ≥ 11.
However, these two results are contradictory (as x cannot be both less than 9 and greater than or equal to 11 simultaneously). So, there is no solution to this system of inequalities.