Question

name: ____________ core: ____
algebra vocabulary practice b
directions: choose the best answer for each.

1. which of the following best describes the circled part of the number sentence ( 9x - 4 = circled{28} )?

a) variable b) term c) coefficient d) equation

1. which of the following is an equation?

a) ( 3x ) b) ( 5 + 6a - 12 ) c) ( 3x^2 + 8 = 6x ) d) ( 5(7a + 2b) )

1. identify each number sentence that contains a coefficient of 7.

( 7a = 14 ) ( 3 + 2x = 7 ) ( 3 + 7y = 12 ) ( 7 - a = 4 )

Explanation:

Question 1

Step1: Recall Algebra Vocabulary

• Variable: A symbol (usually a letter) representing an unknown number (e.g., \( x \) in \( 9x - 4 = 28 \)).
• Term: A single number, variable, or product of numbers and variables (e.g., \( 9x \), \( -4 \), \( 28 \)).
• Coefficient: A number multiplied by a variable (e.g., \( 9 \) in \( 9x \)).
• Equation: A mathematical sentence with an equal sign, showing two expressions are equal (e.g., \( 9x - 4 = 28 \) as a whole).

Step2: Analyze the Circled Part (\( 28 \))

The circled part is \( 28 \), which is a single number, so it is a term. It is not a variable (no letter), not a coefficient (no variable multiplied by it), and not the whole equation (just a part of the equation).

Step1: Recall Definition of Equation

An equation is a mathematical statement that two expressions are equal, containing an equal sign (\( = \)).

Step2: Analyze Each Option

• a) \( 3x \): An expression (no equal sign).
• b) \( 5 + 6a - 12 \): An expression (no equal sign).
• c) \( 3x^2 + 8 = 6x \): Contains an equal sign, so it is an equation.
• d) \( 5(7a + 2b) \): An expression (no equal sign).

Step1: Recall Definition of Coefficient

A coefficient is a number multiplied by a variable (e.g., in \( 7a \), \( 7 \) is the coefficient of \( a \)).

Step2: Analyze Each Number Sentence

• \( 7a = 14 \): The term \( 7a \) has coefficient \( 7 \) (multiplied by \( a \)).
• \( 3 + 2x = 7 \): The coefficient of \( x \) is \( 2 \), and \( 7 \) is a constant (not a coefficient here).
• \( 3 + 7y = 12 \): The term \( 7y \) has coefficient \( 7 \) (multiplied by \( y \)).
• \( 7 - a = 4 \): \( 7 \) is a constant, not a coefficient (no variable multiplied by it).

So the number sentences with a coefficient of \( 7 \) are \( 7a = 14 \) and \( 3 + 7y = 12 \).

Answer:

b) Term

Question 2