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For how many integers will 4x + 5 be greater than 4 and less than 175?

User INulty
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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.

User MonsieurBelbo
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