2.1 Notation, Vocabulary, and Manipulation

• A constant is a fixed number that does not change.


  True
• Match the algebraic notation with its definition:

  Variable ↔️ Represents an unknown quantity

  Constant ↔️ A fixed number

  Coefficient ↔️ Number multiplying a variable

  Index ↔️ Power to which a base is raised
• A term is a single part of an expression separated by addition or subtraction.


  True
• Simplifying an expression means reducing it to its most compact form.

  True
• What is the rule for raising powers to powers?

  Multiply the indices
• What happens to the indices when multiplying terms with the same base?

  They are added
• When raising a power to another power, the indices are multiplied
• When solving two-step equations, inverse operations must be applied in order
• Match the algebraic notation with its definition:

  Variable ↔️ A letter representing an unknown quantity

  Coefficient ↔️ The number multiplying a variable

  Index ↔️ The power to which a base is raised
• An expression does not include an equals sign
• What is the result of combining like terms in the expression \(3x + 2x\)?

  5x
• Two-step equations require two inverse operations to isolate the variable.


  True
• Understanding algebraic notations is essential for manipulating algebraic expressions.


  True
• Like terms have the same variables raised to the same powers.

  True
• Match the algebraic notation with its definition:

  Variable ↔️ Letter representing an unknown

  Constant ↔️ Fixed number that does not change
• Order the steps to solve a one-step equation:

  1️⃣ Apply a single inverse operation

  2️⃣ Simplify the equation

  3️⃣ Solve for the variable
• When solving an equation, it is important to maintain equality on both sides.
• A variable is a letter or symbol that represents an unknown quantity
• An index is the power to which a base is raised
• An expression is a combination of variables, constants, and operations but without an equals sign
• Combining like terms involves adding or subtracting terms with the same variables and powers
• When dividing terms with the same base, the indices are subtracted
• When raising a power to another power, the indices are multiplied.


  True
• What is the solution to the one-step equation \(x + 3 = 5\)?

  x = 2
• Maintaining equality is essential when solving algebraic equations.


  True
• What is the index in the expression \(x^2\)?

  2
• Match the algebraic manipulation with its definition:

  Combining Like Terms ↔️ Adding or subtracting terms with the same variables and powers

  Simplifying Expressions ↔️ Reducing an expression to its simplest form
• When multiplying powers with the same base, the indices are added.


  True
• When multiplying powers with the same base, the indices are added
• The index in algebraic notation represents the power to which a base is raised.
• An algebraic expression does not include an equals sign.
• Simplifying an expression involves combining like terms and applying the order of operations.
• Dividing powers with the same base involves subtracting their indices.

  True
• What is the inverse operation of addition in equation solving?

  Subtraction
• What is the coefficient in the expression `3x`?

  3
• What is an equation in algebraic vocabulary?

  A statement of equality
• What are like terms?

  Terms with the same variables and powers
• What happens to indices when multiplying terms with the same base?

  They are added
• When dividing terms with the same base, the indices are subtracted
• One-step equations are solved using a single inverse operation.


  True