Algebra Basics: Variables and Simple Equations

Variables

• A variable is a letter or symbol that represents a value that can change.
• Variables are used to represent unknown values or values that can vary.
• Examples of variables: x, y, z, a, b, c, etc.

Simple Equations

• A simple equation is an equation that contains only one variable and can be written in the form: ax = b
• Where 'a' is a coefficient (a number) and 'x' is the variable.
• Examples of simple equations: 2x = 4, x + 3 = 5, 4y = 12

Adding/Subtracting Like Terms

• Like terms are terms that have the same variable(s) and coefficient(s).
• When adding or subtracting like terms, the variables and their coefficients are combined.
• Examples:
  1. 2x + 3x = 5x (adding like terms)
  2. 4y - 2y = 2y (subtracting like terms)
  3. x + 2x + 3x = 6x (combining like terms)

Real-life Applications

• Algebraic expressions are used to model real-life situations, such as:
  1. Cost: 2x + 5 represents the cost of 2 items at x dollars each, plus a 5-dollar shipping fee.
  2. Area: A = l × w represents the area of a rectangle with length l and width w.
  3. Motion: d = rt represents the distance traveled (d) at a rate (r) for a time (t).
  4. Science: F = ma represents the force (F) of an object with mass (m) and acceleration (a).
• Algebraic expressions help us solve problems, make predictions, and understand relationships between variables in various fields.

Variables

• Variables are letters or symbols that represent values that can change.
• They are used to represent unknown values or values that can vary.
• Examples of variables include x, y, z, a, b, c, and so on.

Simple Equations

• A simple equation is an equation that contains only one variable.
• It can be written in the form ax = b, where 'a' is a coefficient (a number) and 'x' is the variable.
• Examples of simple equations include 2x = 4, x + 3 = 5, and 4y = 12.

Adding/Subtracting Like Terms

• Like terms are terms that have the same variable(s) and coefficient(s).
• When adding or subtracting like terms, the variables and their coefficients are combined.
• Examples of combining like terms include:
  • 2x + 3x = 5x (adding like terms)
  • 4y - 2y = 2y (subtracting like terms)
  • x + 2x + 3x = 6x (combining like terms)

Real-life Applications

Cost Modeling

• Algebraic expressions can be used to model costs, such as 2x + 5, which represents the cost of 2 items at x dollars each, plus a 5-dollar shipping fee.

Geometry

• Algebraic expressions can be used to calculate the area of a rectangle, represented by A = l × w, where l is the length and w is the width.

Motion

• Algebraic expressions can be used to calculate the distance traveled, represented by d = rt, where d is the distance, r is the rate, and t is the time.

Science

• Algebraic expressions can be used to calculate the force of an object, represented by F = ma, where F is the force, m is the mass, and a is the acceleration.

Importance of Algebraic Expressions

• Algebraic expressions help us solve problems, make predictions, and understand relationships between variables in various fields.

Learn about variables, simple equations, and how to add or subtract like terms in algebra. Understand the concept of variables and how to solve simple equations.