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Algebra Basics Summary

Sep 17, 2025

Overview

This review covers key vocabulary and fundamental principles of algebra, including algebraic expressions, evaluating expressions, ordering integers, and solving one- and two-step equations, as well as basic word problems.

Vocabulary & Key Concepts

  • Absolute value measures a number’s distance from 0 on a number line.
  • An additive inverse is the opposite of a number.
  • An algebraic expression contains at least one variable.
  • A coefficient multiplies the variable in an algebraic expression.
  • A constant is a quantity that does not change.
  • To evaluate means to find the value of a numerical or algebraic expression.
  • An integer is a whole number or its opposite.
  • Inverse operations undo each other.
  • A variable is a symbol representing a quantity that can change.

Algebraic Expressions

  • Translate word phrases into algebraic expressions by identifying variables, constants, and operations.
  • Change algebraic expressions into word phrases by describing the operations and quantities involved.

Substituting & Evaluating

  • Substitute given values for variables in algebraic expressions to solve for a numerical result.

Ordering Integers

  • List integers from least to greatest by comparing their values on a number line.

Evaluating Expressions

  • Apply arithmetic operations (addition, subtraction, multiplication, division) to evaluate expressions given.

Adding and Subtracting Integers

  • Combine integers by following the rules for addition and subtraction of positive and negative numbers.

Multiplying and Dividing Integers

  • Multiply or divide integers, using the rule that like signs give a positive result and unlike signs give a negative result.

Solving One-Step Equations

  • Isolate the variable by applying the inverse operation (addition, subtraction, multiplication, or division) to both sides of the equation.

Solving Two-Step Equations

  • Undo addition/subtraction and multiplication/division in order to solve for the variable in equations with two steps.

Story Problems

  • Use algebraic reasoning to translate real-world problems into expressions or equations and solve for unknowns.

Key Terms & Definitions

  • Absolute value — a number’s distance from 0 on a number line.
  • Additive inverse — the opposite of a number.
  • Algebraic expression — an expression with at least one variable.
  • Coefficient — the number multiplied by the variable.
  • Constant — a value that does not change.
  • Evaluate — to find the value of an expression.
  • Integer — a whole number or its opposite.
  • Inverse operation — operations that undo each other.
  • Variable — a symbol representing a changeable value.

Action Items / Next Steps

  • Review vocabulary definitions and ensure you can match each term.
  • Practice translating word phrases to algebraic expressions and vice versa.
  • Complete the evaluating, ordering, and solving equations practice problems.
  • Solve the story problems, showing your work for each step.