Introductory and Intermediate Algebra MATH001

A series of vocabulary flashcards covering key concepts from the Introductory and Intermediate Algebra MATH001 course.

Equation

A number sentence that states that the expressions on either side of the equals sign represent the same number.

Solution of an Equation

Any replacement for the variable that makes an equation true.

Equivalent Equations

Equations that have the same solutions.

Addition Principle

For any real numbers a, b, and c, a = b is equivalent to a + c = b + c.

Multiplication Principle

For any real numbers a, b, and c with c ≠ 0, a = b is equivalent to a • c = b • c.

Inequality

A number sentence containing > (is greater than), < (is less than), ≥ (is greater than or equal to), or ≤ (is less than or equal to).

Solution of an Inequality

A replacement that makes an inequality true.

Percent

A ratio expressed as a fraction of 100.

Formula

An equation that expresses a relationship between two or more quantities.

Application Problem

A problem that applies mathematical concepts to real-world scenarios.

Graph of an Inequality

A drawing that represents the solutions of an inequality on a number line.

No Solution

A situation where an equation has no values that satisfy it.

Infinitely Many Solutions

A situation where an equation holds true for all values of the variable.

Five Steps for Problem Solving in Algebra

1. Familiarize yourself with the problem. 2. Translate the problem to an equation. 3. Solve the equation. 4. Check the answer. 5. State the answer clearly.

Distributive Law

A property that allows a term to be multiplied across a sum or difference.

Collecting Like Terms

Combining terms that have the same variable raised to the same power.

Applications of Percent Problems

Problems that involve calculations based on percentage relationships.

Self-Study

A learning activity that allows students to practice concepts independently.

Translation in Inequalities

The process of converting words or phrases into mathematical symbols or expressions.

At Least / At Most

'At least' indicates a lower bound while 'at most' indicates an upper limit.