Final answer:
To find the number of integers that make the expression 4x+12 greater than 10 and less than 210, set up and solve the inequality -0.5 < x < 49.5.
Step-by-step explanation:
To determine how many integers will make the expression 4x+12 greater than 10 and less than 210, we can set up the following inequality:
10 < 4x+12 < 210
Subtract 12 from all parts of the inequality:
-2 < 4x < 198
Divide all parts of the inequality by 4:
-0.5 < x < 49.5
The solution is all the integers between -1 and 49, excluding -1 and 49. Therefore, there are 47 integers that satisfy the inequality.