2.1 Notation, Vocabulary, and Manipulation

• Algebraic notation uses letters to represent unknown quantities called variables
• A fixed numerical value in algebraic notation is called a constant
• A combination of variables, constants, or both is called a term
• A variable in algebraic vocabulary is always represented by a letter.

  True
• The coefficient in the term 2x is 2.


  True
• Algebraic notation allows for the concise representation of mathematical relationships.


  True
• A variable is represented by a letter and represents a fixed numerical value.

  False
• A coefficient is a number that multiplies a variable.


  True
• Match the algebraic element with its description:

  Variable ↔️ Letter representing unknown quantity

  Coefficient ↔️ Number multiplying a variable

  Constant ↔️ Fixed numerical value

  Term ↔️ Combination of variables and constants
• Understanding algebraic notation is crucial for manipulating and solving algebraic equations
• In the expression 2x + 5, the constant is 5
• A variable, constant, or product of both is referred to as a term
• Match the algebraic term with its example:

  Variable ↔️ x in 2x + 5

  Constant ↔️ 5 in 2x + 5

  Coefficient ↔️ 2 in 2x + 5

  Term ↔️ 2x and 5 in 2x + 5
• Like terms have the same variables raised to the same powers.

  True
• The expression 3x + 2y - x + 5y simplifies to 2x + 7y.


  True
• Steps to simplify an algebraic expression:

  1️⃣ Identify like terms

  2️⃣ Combine their coefficients

  3️⃣ Retain the variable and power
• Factorizing involves rewriting an expression as a product of common factors.


  True
• Steps to factorize an algebraic expression:

  1️⃣ Identify the common factor

  2️⃣ Write the expression as a product of the common factor and remaining terms
• What does algebraic notation use to represent mathematical relationships?

  Symbols and quantities
• What is a fixed numerical value in algebraic notation called?

  Constant
• What is a variable, constant, or combination of both in algebraic notation called?

  Term
• Match the algebraic term with its description:

  Variable ↔️ Letter representing an unknown quantity

  Constant ↔️ Fixed numerical value

  Coefficient ↔️ Number multiplying a variable

  Term ↔️ Variable, constant, or product of both

  Expression ↔️ Combination of terms with operators
• Like terms have the same variables raised to the same powers.


  True
• Expanding algebraic expressions involves removing parentheses
• Match the algebraic process with its description:

  Expand ↔️ Multiply term outside parentheses by each inside

  Factorize ↔️ Identify common factors and express as a product
• Steps to solve a linear equation:

  1️⃣ Simplify both sides

  2️⃣ Isolate the variable

  3️⃣ Divide by the coefficient
• When multiplying or dividing an inequality by a positive number, the inequality sign remains the same.


  True
• Algebraic simplification involves combining like terms in an algebraic expression.
• Algebraic simplification is the process of making an algebraic expression shorter and easier to work with.
• Expanding algebraic expressions involves removing parentheses by multiplying the outside term by each term inside.
• The factorization of 2x + 6 is 2(x + 3).
• Match the algebraic process with its description:

  Expand ↔️ Remove parentheses by multiplying

  Factorize ↔️ Express as a product of common factors
• A letter that represents an unknown quantity is called a variable
• A coefficient is a number that multiplies a variable.

  True
• A combination of terms connected by operators is called an expression
• What is algebraic simplification the process of making an expression?

  Shorter
• Steps to simplify an algebraic expression:

  1️⃣ Identify like terms

  2️⃣ Combine coefficients

  3️⃣ Retain the variable and power
• What is the process of breaking down an expression into its factors called?

  Factorizing
• What is the first step to solve a linear equation?

  Simplify both sides
• When multiplying or dividing an inequality by a negative number, the inequality sign must be reversed