Question

Find a and b. If 15 < 5x < 30, then a < x². Determine the values of a and b.

Answer 1

To find the values of a and b, solve the given inequality and equation. The values of a can be any real number less than 9, and the values of b can be any real number less than 36.

Step-by-step explanation:

To find the values of a and b, we need to solve the given inequality and equation:

1. 15 < 5x < 30
2. a < x²

From the first inequality, we can divide all sides by 5 to get 3 < x < 6. This means that x is greater than 3 and less than 6.

Substituting x = 3 and x = 6 into the second inequality, we get:

1. a < 9
2. a < 36

Therefore, the values of a can be any real number less than 9, and the values of b can be any real number less than 36.