Solving Equations and Inequalities (Vocab Flashcard)

Front

What is a set in mathematics?

Back

A collection of distinct objects, considered as an object in its own right. Example: {1, 2, 3, 4}

Front

What is an irrational number?

Back

A number that cannot be expressed as a fraction a/b where a and b are integers; it has a non-repeating, non-terminating decimal expansion. Example: √2.

Front

What is a rational number?

Back

A number that can be expressed as a fraction a/b where a and b are integers. Example: 7⅞.

Front

What does it mean for one set to be a subset of another?

Back

A set A is a subset of set B if all elements of A are also elements of B. Example: If A={1,2} and B={1,2,3}, then A is a subset of B.

Front

What is a compound inequality?

Back

An inequality that combines two or more inequalities. Example: x > 2 and x < 5.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another. Example: x + 2 = 5 (equation) vs x + 2 < 5 (inequality).

Front

What is the solution set of an inequality?

Back

The set of all values that satisfy the inequality. Example: For x > 3, the solution set is all numbers greater than 3.

Front

What does it mean for two sets to be equal?

Back

Two sets A and B are equal if they contain exactly the same elements. Example: A={1,2} and B={2,1} are equal.

Front

What is a number line?

Back

A visual representation of numbers on a straight line, where each point corresponds to a number. Used to illustrate inequalities.

Front

What is the union of two sets?

Back

The union of sets A and B is the set of elements that are in A, in B, or in both. Example: A={1,2} and B={2,3} gives A ∪ B={1,2,3}.