Am I going in the right direction for this question

Question

Question: three less than the product of a number, n, and five is less than 32. Find the range of the values for the number

my answer? 5n - 3 < 32

Answer 1

Yeppers product is the result of multiplication, and we write 5 times n as 5n. Three less than that is 5n - 3 aaaaand it's less than 32, so 5n - 3 < 32.

To solve for n, you do it just as though the < was an =. The only difference is that dividing by a negative coefficient reverses the sign.

For example...

-6n - 3 ≤ 33

-6n ≤ 36

n ≥ - 6

To show this, let's pick a number less than -6, like -7.

-6(-7) ≤ 33

42 ≤ 33

Well, duh, that's not true, but let's use 0, which is greater than -6.

-6(0) ≤ 33

0 ≤ 33

There ya go. Thaaaat's true. Always reverse the sign when dividing by a negative coefficient.