Question

5 vocabulary review

• review the unit vocabulary. put a check mark by items you can use in speaking and writing. look up the meaning of any terms you do not know.

math vocabulary
☐ dependent variable ☐ like terms
☐ equivalent expressions ☐ solution of an equation
☐ independent variable ☐ variable
academic vocabulary
☐ algebraics
☐ depend on
☐ substitute
☐ verify

• use the unit vocabulary to complete the problems.

1 a student is buying thank you cards. each thank you card costs $2. the equation t = 2c represents the total cost, t, this student will spend to buy c cards. which variable is the independent variable in the equation? which is the dependent variable? explain how you know.
2 what is a solution of an equation? explain one way to check a solution of an equation. use at least four math or academic vocabulary terms in your explanation. underline each term you use.
3 explain one way each pair of terms is related.
a. like terms and equivalent expressions
b. variable and algebraic

Explanation:

Problem 1

Step1: Recall variable definitions

Independent variable: the one you can choose/control. Dependent variable: depends on the independent one.

Step2: Analyze the equation \( t = 2c \)

• \( c \): number of cards (student chooses how many to buy, so controlled).
• \( t \): total cost (depends on how many cards, since \( t = 2 \times c \)).

Step1: Define solution of an equation

A solution of an equation is a value (or set of values) for the \(\underline{\text{variable}}\) that makes the equation true (when substituted, both sides are \(\underline{\text{equivalent expressions}}\)).

Step2: Explain checking a solution

To check, \(\underline{\text{substitute}}\) the solution into the equation. Calculate both sides. If they are equal, the value \(\underline{\text{verifies}}\) as a solution. For example, in \( x + 3 = 5 \), solution \( x = 2 \). Substitute: \( 2 + 3 = 5 \) (left = right, so verified).

Step1: Analyze "like terms" and "equivalent expressions"

• Like terms: terms with same variable (or constant) that can be combined (e.g., \( 3x \) and \( 5x \)).
• Equivalent expressions: expressions that have the same value for all variable values. Combining like terms is a way to form equivalent expressions (e.g., \( 3x + 5x = 8x \), so \( 3x + 5x \) and \( 8x \) are equivalent).

Answer:

Independent variable: \( c \) (number of cards, as the student decides how many to buy). Dependent variable: \( t \) (total cost, as it depends on the number of cards \( c \) bought, calculated by \( t = 2c \)).

Problem 2