Study guide: Linear Equations in One Variable

📋 Course Outline

1. Variables and Algebraic Equations
2. Recognizing Linear Equations
3. Equations and Statements
4. Balancing Both Sides

📖 1. Variables and Algebraic Equations

🔑 Key Concepts & Definitions

• Algebraic equation: an equality that contains one or more variables

★ Must-know

📌 A numerical equation contains known numbers, whereas an algebraic equation expresses an equality using one or more variables.

Further detail

• To identify the variable in an equation, locate the letter or letters whose values are unknown.

• The numerical equation 7 + 7 = 12 can be expressed using a variable by replacing an unknown number with a letter.

💡 Memory Hook

A numerical equation has known numbers, whereas an algebraic equation includes a variable.

📖 2. Recognizing Linear Equations

🔑 Key Concepts & Definitions

• Linear equation: an equation in which the maximum power of any variable is 1

★ Must-know

• The equation 5x² + 4y = 0 is not linear because the power of x is 2, which is greater than 1.

• The equation 3x + 4y = 8z – 2x is linear because all variables x, y, and z have a maximum power of 1.

Further detail

📌 A linear equation may contain more than one variable, and a variable may occur on either side or on both sides of the equality sign.

• The listed equations include:
  • 5p + 7 = 22
  • y/2 − 1 = 5
  • (3/4)q = 9
  • 3x + y = 5

💡 Memory Hook

Power 1: linear means every variable has maximum power 1.

📖 3. Equations and Statements

★ Must-know

• An equation can be converted into a statement by expressing the equality in words.

Further detail

• The equation-to-statement activity asks learners to express given equations as verbal statements.

📖 4. Balancing Both Sides

🔑 Key Concepts & Definitions

• Solution of a linear equation: obtained by applying balancing operations to eliminate constants while preserving equality

★ Must-know

• To solve an equation using the balancing method, both sides of the equation must be balanced while constants are terminated or eliminated.

Further detail

📌 Any operation used to eliminate a constant in an equation must be performed in a way that keeps the two sides balanced.

💡 Memory Hook

Eliminating constants while balancing both sides leads to the solution of the equation.