(Part of math unit test) Compound inequalities and Absolute Value Inequalities

Compound inequality

• A conjunction of two or more inequalities

• The set of solutions for a compound inequality are the values that make all of the inequalities true

When do we use the term “and”

• We use “and” to indicate that a value must satisfy both inequalities in order to be a solution set

• Written as a ≤ x ≤ b

• ex. x < 3 and x ≥ -2

• ⬆ Can also be written as -2 ≤ x < 3

When do we use the term “or”

• We use “or” to indicate the value only needs to satisfy at least one inequality in order to be the solution set

• Written as x < a or x < b

• Ex. x > 3 or x ≤ -2

Interval

A set of numbers that lie between two values

Interval notation

• A way to represent a solution or interval as a pair of numbers using a combination of square brackets and parentheses

• Ex.

  • Inequality notation: x ≥ 3

  • Interval notation: [ 3, ∞ )

Absolute value inequality

An inequality containing the absolute value of a variable expression

What is absolute value sometimes called?

Magnitude

Solutions to absolute value inequalities usually involve multiple ______

inequalities

For absolute value inequalities with an algebraic expression ____ and ____

• p(x)

• k > 0

| p(x) | < k is within ___ spaces of ___ and can be written as __________

• k

• 0

• -k < p(x) < k

| p(x) | > k is more than ___ spaces of ___ and can be written as __________

• k

• 0

• p(x) < -k or p(x) > k

For the absolute inequality a | p(x) | + b < c, the expression ______ must be isolated using _____ operations before rewriting the inequality as a compound inequality.

• | p(x) |

• inverse

And vs. Or equation

• And → < or ≤ Less thAND

• Or → > or ≥ GreatOR