How are markdowns and discounts related

You'd have to check your reference material (text, on-line tutor) for the "official" definitions of each.

In my experience, both are a reduction in price. Whether the reduction is called a markdown or a discount may depend on the reason for it.

A discount may be part of a general pricing structure or plan: a customer may obtain a discount for paying in cash, paying within a particular time period, as part of a promotion or benefit (new-customer or employee discount, for example).  Goods that are "on sale" may be advertised as having a particular "discount."

A markdown may be a reduction in price because goods are damaged, out-of-date (unfashionable, or near/beyond their expiration date), or for the purpose of reducing unwanted inventory. A discount on items that "must go," or a reduction in price to better match market conditions, may be called a markdown—a reduction in the asking price of real estate, for example.

4|x| - 1 < -4

we are given with absolute value inequality

lets make the absolute value alone

4|x| - 1 < -4

add 1 on both sides

4|x| - 1 +1 < -4 +1

4|x|   < -3

now divide by 4 on both sides

any absolute value cannot be negative.

absolute value function gives only the positive value.

so there is no solution for this problem.

there is no solution for this so its not possible to graph this inequality.