Julia's hair is 4 cm long. Her hair grows 1.5 cm per month. Julia wants her hair to grow to at least 7 cm long.

Write an inequality to determine the number of months, $ m $, it will take for Julia's hair to be at least 7 cm long. What is the minimum number of months Julia must wait?

A. $ 4 + 1.5m > 7 $

B. $ 5.5m \geq 7 $

C. $ 1.5m + 4 \geq 7 $

D. $ 1.5 + 4m \geq 7m $

The correct inequality representing the duration it will take Julia's hair to grow to at least 7cm is 1.5m + 4 >= 7. By solving this inequality, we find that Julia must wait for at least 2 months to achieve the desired hair length.

Explanation:

The question involves creating an inequality to calculate the time it will take for Julia's hair to grow to a certain length. The answer should describe the hair's initial length, the rate of hair growth per month, and the desired hair length.

Julia's hair is 4cm long initially, and it grows 1.5cm each month. She wants her hair to grow to at least 7cm long. We represent the months as m.

So, for her hair to be at least 7cm long, the sum of her hair's initial length and the product of the rate of growth and time should be equal to or greater than 7. This can be expressed as an inequality: 1.5m + 4 >= 7.

To find the minimum number of months it would take, we solve for m: (7-4) / 1.5 = 2. Therefore, it will take Julia at least 2 months for her hair to grow to be at least 7cm long.

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