Algebra 1 Unit 1 Mastery Test

Questions and Answers

What is the Property of Equality?

Multiply the same number on each side of the equal sign.

Subtract the same number from the right side of the equal sign.

Add, subtract, multiply, or divide the same number on each side of the equal sign. (correct)

Add the same number to one side of the equation only.

What is the Addition Property of Equality?

If a = b, then a + c = b + c.

What is the Subtraction Property of Equality?

If a = b, then a - c = b - c.

What is the Multiplication Property of Equality?

If a = b and c ≠ 0, then a • c = b • c. Signup and view all the answers

What is the Division Property of Equality?

If a = b and c ≠ 0, then a ÷ c = b ÷ c. Signup and view all the answers

What is an Inverse Operation?

The opposite or reverse operation. Signup and view all the answers

What is the Inverse Operation of Subtraction?

Addition. Signup and view all the answers

What is the Inverse Operation of Addition?

Subtraction. Signup and view all the answers

What is the Inverse Operation of Multiplication?

Division. Signup and view all the answers

What is the Inverse Operation of Division?

Multiplication. Signup and view all the answers

What does the equation x + 6 = -4 represent?

Given. Signup and view all the answers

What is the meaning of x + 6 = -4 in terms of the Property of Equality?

It demonstrates the property of equality. Signup and view all the answers

What does x + 0 = -10 represent?

Inverse. Signup and view all the answers

What does the equation x = -10 signify?

Identity. Signup and view all the answers

What is an equation?

A mathematical statement that two expressions are equal. Signup and view all the answers

What does it mean to solve an equation?

To find the solution. Signup and view all the answers

What is a solution in the context of algebra?

The value that makes an equation true. Signup and view all the answers

What are inverse operations?

Operations that undo each other. Signup and view all the answers

What does it mean to isolate the variable?

To get a variable alone on one side of an equation. Signup and view all the answers

What are linear equations in one variable?

An equation which can be written in the form ax + b = c. Signup and view all the answers

How are terms separated in an equation?

By addition and subtraction signs. Signup and view all the answers

What are like terms?

Terms with the same variable and exponent. Signup and view all the answers

What is a coefficient?

The numerical part of a term. Signup and view all the answers

How can coefficients of like terms be combined?

By adding or subtracting. Signup and view all the answers

What is a constant in algebra?

A number with no variable. Signup and view all the answers

What does identity mean in algebra?

All real solutions for x + 1 = x + 1. Signup and view all the answers

What does conditional refer to in algebra?

X = #, an equation that is true for some values. Signup and view all the answers

What is a contradiction in algebra?

An empty set, no solution. Signup and view all the answers

What is an equation that is false for every solution?

A contradiction. Signup and view all the answers

Study Notes

Properties of Equality

The Property of Equality allows performing the same operation on both sides of an equation to maintain balance.
The Addition Property states: If ( a = b ), then ( a + c = b + c ).
The Subtraction Property states: If ( a = b ), then ( a - c = b - c ).
The Multiplication Property states: If ( a = b ) and ( c \neq 0 ), then ( a \cdot c = b \cdot c ).
The Division Property states: If ( a = b ) and ( c \neq 0 ), then ( a \div c = b \div c ).

Inverse Operations

An inverse operation is the reverse of a given operation, used for solving equations.
Inverse of subtraction is addition.
Inverse of addition is subtraction.
Inverse of multiplication is division.
Inverse of division is multiplication.

Solving Equations

Solving an equation involves finding a value (solution) that makes it true.
An equation is a mathematical statement asserting that two expressions are equal.
To isolate the variable means getting it alone on one side of the equation for resolution.

Types of Equations

Linear equations in one variable can be written in the form ( ax + b = c ).
Terms in an equation are separated by addition and subtraction signs.
Like terms have the same variable and exponent and can be combined by adding or subtracting.

Essential Definitions

A coefficient is the numerical factor of a term.
A constant is a specific number without a variable.
An identity indicates that an equation is true for all real numbers, such as ( x + 1 = x + 1 ).
A conditional equation is true for certain values, exemplified by ( 2x - 5 = 9 ) only being true for ( x = 7 ).
A contradiction arises when an equation has no solutions, represented as an empty set.

Further Concepts

Inverse operations undo each other, facilitating equation solving.
The term "solution" refers to the value that satisfies the equation.
A contradiction signifies that no value can satisfy the given equation, such as ( x + 1 = x + 2 ), which has no solution.

Key Equation Examples

Given: ( x + 6 = -4 )
To isolate ( x ), apply properties of equality.
Result: ( x = -10 ) demonstrates both identity and solving principles.

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Description

Test your understanding of key algebraic properties with this mastery quiz. Focus on the properties of equality, including addition, subtraction, and multiplication. Perfect for reinforcing foundational concepts in Algebra 1.