Question

the sum of two postitive integers, a and b, is least 30. the difference of the two integers is at least 10. if b is the greater integer, which system of inequalities could represent the values of a and b.​

Answer 1

The right system is a + b ≥ 30 , b ≥ a + 10

Explanation:

∵ The sum of them is at least 30 means the smallest value is 30

∴ Their sum is a + b = 30 or greater than 30

∴ a + b ≥ 30

∵ Their difference is at least 10 and the greater is b

∴ b - a = 10 or greater than 10

∴ b - a ≥ 10

∴ b ≥ a + 10

So the right system is the first answer

a + b ≥ 30 , b ≥ a + 10