Algebra 1.1 Assignment: Variables and Expressions

Questions and Answers

What is an algebraic expression?

A mathematical phrase that cannot be determined true or false

A numerical value

A mathematical expression containing one or more variables (correct)

A letter or symbol used to represent an unknown

What is the definition of a coefficient?

The constant preceding the variables in a product (correct)

An unknown quantity

A mathematical phrase

A constant value

What is a constant?

A numerical value

What is an expression?

A mathematical phrase that cannot be determined true or false Signup and view all the answers

What is a variable?

A letter or symbol used to represent an unknown Signup and view all the answers

If x is 5, then 6x = _____.

30 Signup and view all the answers

What is the expression for the sum of n and five?

n + 5 Signup and view all the answers

What is the expression for five subtracted from n?

n - 5 Signup and view all the answers

What is the expression for eight added to x?

x + 8 Signup and view all the answers

What is the expression for eight subtracted from x?

x - 8 Signup and view all the answers

What is the expression for eight minus x?

8 - x Signup and view all the answers

What is the expression for five minus n?

5 - n Signup and view all the answers

What is the expression for x added to the sum of five and seven?

x + (5 + 7) Signup and view all the answers

What is the expression for the sum of eight and two, subtracted from x?

x - (8 + 2) Signup and view all the answers

What is the expression for the difference of eight and two, added to x?

x + (8 - 2) Signup and view all the answers

What is the expression for the sum of x and itself?

x + x Signup and view all the answers

Which expression does not represent 'the sum of n and 6'?

6n Signup and view all the answers

Which of the following expressions represents 'the difference of 8 and n'?

8 - n Signup and view all the answers

Which of the following expressions does not represent 'four more than one-third x'?

1/4x + 3 Signup and view all the answers

Which of the following expressions represents 'twelve diminished by six times a number'?

12 - 6n Signup and view all the answers

Which of the following expressions represents 'three times the difference between t and y'?

3(t - y) Signup and view all the answers

Which of the following expressions represents 'the quotient of nine times a number and seven'?

9n ÷ 7 Signup and view all the answers

Which of the following expressions represents 'the sum of n and the sum of 8 and 6'?

n + (8 + 6) Signup and view all the answers

The coefficient of 6x is _____.

6 Signup and view all the answers

The coefficient of 8 + 2N is _____.

16 Signup and view all the answers

The coefficient of 9(14)P is _____.

126 Signup and view all the answers

The coefficient of 2(3)(6)Q is _____.

36 Signup and view all the answers

Look at each expression. Is it equivalent to 'the quotient of 10 plus x and y minus 3'?

(10+x)/(y-3) Signup and view all the answers

For 3x^2 - 4x + 1, match the following:

x = Variable 3 = Coefficient 1 = Constant 3x^2 - 4x + 1 = Algebraic Expression 2 = Degree Signup and view all the answers

Study Notes

Key Definitions

Algebraic Expression: A mathematical expression that includes one or more variables.
Coefficient: The constant factor that multiplies a variable in an expression.
Constant: A fixed numerical value not affected by variables.
Expression: A mathematical phrase that represents a value but cannot be classified as true or false.
Variable: A symbol or letter that stands for an unknown number.

Mathematical Operations with Variables

Example when x = 5: Substituting gives ( 6x = 30 ).
The sum of ( n ) and five: Written as ( n + 5 ).
Five subtracted from ( n ): Written as ( n - 5 ).
Eight added to ( x ): Expressed as ( x + 8 ).
Eight subtracted from ( x ): Expressed as ( x - 8 ).
Eight minus ( x ): Presented as ( 8 - x ).
Five minus ( n ): Expressed as ( 5 - n ).
( x ) added to the sum of five and seven: Written as ( x + (5 + 7) ).
The sum of eight and two, subtracted from ( x ): Written as ( x - (8 + 2) ).
The difference of eight and two, added to ( x ): Expressed as ( x + (8 - 2) ).
The sum of ( x ) and itself: Written as ( x + x ).

Expression Evaluation and Identification

Incorrect representation of "the sum of ( n ) and 6": ( 6n ) (not ( 6 + n ) or ( n + 6 )).
Correct representation of "the difference of 8 and ( n )": ( 8 - n ) (not ( n - 8 ) or (-8n)).
Incorrect option for "four more than one-third ( x )": ( 1/4x + 3 ).
Correct representation of "twelve diminished by six times a number": ( 12 - 6n ).

Coefficient Analysis

Coefficient of ( 6x ): 6.
Coefficient of ( 8 + 2N ): 16 (from multiplying 8 and 2).
Coefficient of ( 9(14)P ): 126 (product of 9 and 14).
Coefficient of ( 2(3)(6)Q ): 36 (product of 2, 3, and 6).

Expression Equivalence

For expression ( \frac{10 + x}{y - 3} ):
- ( \frac{10+x}{y} ): No
- ( \frac{10+x}{y-3} ): Yes
- ( 10 + \frac{x}{y} - 3 ): No
- ( \frac{10 + x - 3}{y} ): No

Properties of Algebraic Expressions

For the expression ( 3x^2 - 4x + 1 ):
- Variable: ( x ).
- Coefficient: 3 (of the term ( 3x^2 )).
- Constant: 1 (the standalone integer).
- Algebraic Expression: ( 3x^2 - 4x + 1 ).
- Degree: 2 (highest power of variable ( x )).

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