Chapter 6: Inequalities and Absolute Values

real number line

a continuous line that extends from negative infinity through zero to positive infinity

when isolating a variable in an inequality, we find a _________ of possible values, rather than a single value as in an equation

when multiplying or dividing an inequality by a negative number…

reverse the inequality sign

you can add a set of two or more inequalities with one or more variables if the inequality sign

faces the same direction

three part inequalities

express two separate inequalities more concisely

true or false: we can multiply or divide by any variable in inequalities even if the sign is unknown

false

if x² > b then x __ √b

>

if x² > b then x __ -√b

<

if x² ≥ b, then x __√b

≥

if x² < b, then -√b __ x__√b

<, <

if x² ≤ b, then -√b __ x__√b

≤, ≤

if a ≤ x ≤ b and c ≤ y ≤ d then the maximum value of xy will be the

largest of ac, ad, bc, and bd

if a ≤ x ≤ b and c ≤ y ≤ d then the minimum value of xy will be the

the smallest of ac, ad, bc, and bd

when solving equations with absolute values, we solve twice, when the expression inside the bars is

positive and negative

when solving for the negative case of absolute values, you ________- the negative sign to each term

distribute

two absolute values are equal either when the expressions inside the bars are

the same or when they are opposites

when simplifying absolute value inequalities, we test two cases

one when the expression inside the absolute bars is positive and another when it is negative

if an absolute value equation has a variable on both sides of the equal sign check the solutions for _________ roots

extraneous

if the absolute value of an expression is equal to a negative number then the equation has ______ solutions

zero