Final answer:
To find the number of integers that satisfy the inequality 4x + 5 > 4 and 4x + 5 < 175, we solve the inequalities and determine the range of x values. Then, we list out the integers within that range to find the answer.
Step-by-step explanation:
To find the number of integers that satisfy the given condition, we need to solve the inequality 4x + 5 > 4 and 4x + 5 < 175.
Solving the first inequality, we subtract 5 from both sides: 4x > -1.
Dividing both sides by 4, we get x > -1/4.
Solving the second inequality, we subtract 5 from both sides: 4x < 170.
Dividing both sides by 4, we get x < 42.5.
Thus, the integers that satisfy the inequality are -1/4 < x < 42.5.
Since x must be an integer, we can list out the integers within this range: -1, 0, 1, 2, ..., 41, 42.
Therefore, there are 44 integers that satisfy the given condition.