Final answer:
By substituting the equation y=2-x into the inequality 7x+4y>44 and simplifying, we find the range of possible values for x to be all real numbers greater than 12.
Step-by-step explanation:
The question involves solving a system of inequalities using substitution to find the range of possible values for x. We have the inequality 7x + 4y > 44 and the equation y = 2 - x. By substitution, we replace y in the inequality with 2 - x from the given equation, which gives us a new inequality to express x's range of possible values. This requires understanding the concept of linear equations where we use an inequality symbol to show how two metric measurements are related.
To substitute, we get 7x + 4(2 - x) > 44. Simplifying this, we get 7x + 8 - 4x > 44, which becomes 3x > 36. So, dividing both sides by 3, we get x > 12. Hence, the range of possible values for x in the given system is all real numbers greater than 12.