Inequalities and Absolute Value flashcards

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What does inequality symbols mean?One-Variable Inequalities: A comparison representing many possible values.
When is an endpoint included?One-Variable Inequalities: When the symbol contains an equality bar.
How would you define solving by addition?One-Variable Inequalities: An equivalent shift of both sides of an inequality.
Why does addition preserve order?One-Variable Inequalities: Both values move by the same amount.
What is meant by multiplying by a negative?One-Variable Inequalities: A sign-reversing order transformation.
When must the inequality sign reverse?One-Variable Inequalities: When both sides are multiplied or divided by a negative number.
What does intersection with and mean?Compound Inequalities: The overlap of two inequality solution sets.
What does and mean on a number line?Compound Inequalities: Only shared points belong.
How would you define union with or?Compound Inequalities: The combined region of two inequality solution sets.
Can an or solution have two separate rays?Compound Inequalities: Yes, when the conditions point outward.
What is meant by interval notation?Compound Inequalities: A compact notation for sets of real numbers.
Why is infinity never a closed endpoint?Compound Inequalities: It is not a finite real number in the set.
What does absolute value as distance mean?Absolute Value Equations: A nonnegative number-line distance.
Why can |x−c| not equal a negative number?Absolute Value Equations: Distance cannot be negative.
How would you define two-branch equations?Absolute Value Equations: The two possible positions a positive distance d from c.
When is there just one solution?Absolute Value Equations: When the specified distance is zero.
What is meant by extraneous or impossible cases?Absolute Value Equations: A proposed answer that fails the original equation or domain.
Why check both branches?Absolute Value Equations: Transformations or restrictions may invalidate a candidate.
What does inside distance mean?Absolute Value Inequalities: A bounded interval of points within a distance.
What does < do to boundary points?Absolute Value Inequalities: It excludes points exactly d away.
How would you define outside distance?Absolute Value Inequalities: Two regions outside a central interval.
What connector joins the two rays?Absolute Value Inequalities: Or, since either ray works.
What is meant by boundary checks?Absolute Value Inequalities: Checking a solution set using representative inputs.
Why test endpoints separately?Absolute Value Inequalities: Strict and inclusive signs treat them differently.
What does nonnegative quantities mean?Modeling Constraints: A contextual restriction on allowable variable values.
Why state a domain before interpreting an answer?Modeling Constraints: It determines which algebraic values are meaningful.
How would you define capacity bounds?Modeling Constraints: An upper or lower bound expressed by an inequality.
Which symbol matches at most?Modeling Constraints: Less than or equal to.
What is meant by integer solutions?Modeling Constraints: Restricting a continuous solution set to integer counts.
Why round down at a maximum capacity?Modeling Constraints: Rounding up would exceed the bound.