# How do you find two consecutive odd integers such that 2 times the lesser is 19 less than 3 times the greater?

Oct 21, 2016

The numbers are $13 \mathmr{and} 15$

#### Explanation:

Consecutive odd numbers differ by 2.
If the smaller one is called $x$, the larger one will be $x + 2$

We will be working with 2 terms which differ by 19.

This can be written in 3 different ways. Use the form which makes the most sense to you. They are all correct.

$\text{smaller" +19 = "BIGGER"" } \leftarrow$ I will use this one

$\text{BIGGER - smaller} = 19$

$\text{BIGGER" - 19 = "smaller}$

$2 x + 19 = 3 \left(x + 2\right)$

$2 x + 19 = 3 x + 6 \text{ } \leftarrow$ move x terms to one side

$19 - 6 = 3 x - 2 x$

$13 = x$

$x = 13 \text{ } \leftarrow$ the first odd number.

The next odd number is $15$.