Question

the sum of two consecutive odd integers is less than four times the smaller of two integers. What is the value of each integer

Answer 1

Consecutive odd integers differ by 2. For example, 1, 3, 5, 7. The difference is 2

Let x represent the smaller odd integer. This means that the larger consecutive integer is x + 2

From the information given, the sum of two consecutive odd integers is less than four times the smaller of two integers. it means that

`\begin{gathered} x\text{ + x + 2 }<4* x \\ 2x\text{ + 2 }<4x \\ 2\text{ }<4x\text{ - 2x} \\ 2<\text{ 2x} \\ \text{Dividing both sides by 2, } \\ 1\text{ < x} \\ x\text{ > 1} \end{gathered}`

The value of the smaller integer ranges from 2 to infinity. Since 2 is not odd, it starts from 3

The value of the larger integer ranges from 3 + 2 to infinity. Therefore,

The value of the larger integer ranges from 5 to infinity