Business Mathematics and Absolute Value Lecture Notes

This set of vocabulary flashcards covers fundamental business math concepts like revenue and breakeven points, as well as algebraic rules for solving absolute value equations and inequalities.

Revenue

The money that a business makes, often described as "money in."

Breakeven point

The number of units sold where revenue equals cost ($R = C$), resulting in zero profit and zero loss.

Exceeding cost

The state where revenue is greater than the cost ($R > C$), allowing a business to make a profit.

Interval Notation

A methodology for writing solutions where the interval is always read from left to right, going from the smallest value to the largest value.

Absolute Value

The distance a number is from zero on the number line; it must always be positive or zero.

No Solution (Absolute Value)

The outcome when an equation indicates that an absolute value is equal to a negative number, as distance cannot be negative.

$|x| > a$ (where $a > 0$)

A case where the distance from zero is greater than $a$, formulated as $x > a$ or $x < -a$.

$|x| < a$ (where $a > 0$)

A case where the distance from zero is smaller than $a$, resulting in $x$ being "squished" between $-a$ and $a$ ($-a < x < a$).

Union Sign ($\cup$)

A symbol used in interval notation to connect two or more different intervals.

Distribution over Absolute Value

A mathematically incorrect operation; you cannot distribute a number into absolute value bars.

Isolating the Absolute Value

The critical first step in solving absolute value equations or inequalities, ensuring the absolute value bars are by themselves before proceeding.