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Key Algebra Concepts
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Key Algebra Concepts

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@ProlificRetinalite5738

Questions and Answers

What is a constant?

  • An equation
  • A value that does not change (correct)
  • A variable that can change
  • An inequality

    • What is an inequality?

    A mathematical sentence that compares quantities

    What is the solution of an inequality?

    A value that makes the inequality true

    What is a solution set?

    <p>The set of all solutions of an inequality</p> Signup and view all the answers

    What does the graph of an inequality represent?

    <p>Shows the solution set on a number line</p> Signup and view all the answers

    An open circle on a number line includes the point.

    <p>False</p> Signup and view all the answers

    A closed circle on a number line includes that point.

    <p>True</p> Signup and view all the answers

    What are properties of equality?

    <p>&quot;What you do to one side, you do to the other.&quot;</p> Signup and view all the answers

    What happens when you change the direction of the sign?

    <p>If you multiply or divide both sides of an inequality by a negative number, you change the direction of the sign.</p> Signup and view all the answers

    What is a compound inequality?

    <p>Formed by joining two inequalities with 'and' or 'or'</p> Signup and view all the answers

    Greater than means ___

    <p>all the numbers larger than</p> Signup and view all the answers

    Less than means ___

    <p>all the numbers lower than</p> Signup and view all the answers

    Greater than or equal to means ___

    <p>all the numbers larger than or equal to</p> Signup and view all the answers

    Less than or equal to means ___

    <p>all the numbers less than or equal to</p> Signup and view all the answers

    What is an equation?

    <p>A mathematical sentence that contains an equals sign</p> Signup and view all the answers

    What is an expression?

    <p>A mathematical phrase that contains operations, numbers, and/or variables</p> Signup and view all the answers

    What are integers?

    <p>All whole numbers (both positive and negative) and zero</p> Signup and view all the answers

    What are consecutive integers?

    <p>Integers that follow each other in order</p> Signup and view all the answers

    What are like terms?

    <p>Terms that have the same variable raised to the same exponent</p> Signup and view all the answers

    What does infinitely many solutions mean?

    <p>Means that any value for the variable would make the equation true</p> Signup and view all the answers

    What does no solution mean?

    <p>No number solves an equation</p> Signup and view all the answers

    Whole numbers include ___

    <p>Natural numbers and zero</p> Signup and view all the answers

    What is the Addition Property of Equality?

    <p>Adding the same number to both sides of an equation doesn't change the equality of the equation.</p> Signup and view all the answers

    What is the Subtraction Property of Equality?

    <p>Subtracting the same number from both sides of an equation doesn't change the equality of the equation.</p> Signup and view all the answers

    What is the Multiplication Property of Equality?

    <p>Multiplying the same number to both sides of an equation doesn't change the equality of the equation.</p> Signup and view all the answers

    What is the Division Property of Equality?

    <p>Dividing the same number to both sides of an equation doesn't change the equality of the equation.</p> Signup and view all the answers

    What is the Substitution Property of Equality?

    <p>If numbers are equal, substituting one for another doesn't change the equality of the equation.</p> Signup and view all the answers

    What is the Distributive Property?

    <p>The product of a number and a sum is equal to the sum of the individual products of terms.</p> Signup and view all the answers

    What are natural numbers?

    <p>The set of numbers 1, 2, 3, 4...</p> Signup and view all the answers

    What are rational numbers?

    <p>The set of all numbers that can be written as the ratio of two integers with a non-zero denominator</p> Signup and view all the answers

    What are irrational numbers?

    <p>The set of all numbers that cannot be expressed as the ratio of integers</p> Signup and view all the answers

    What are real numbers?

    <p>The set of all rational and irrational numbers</p> Signup and view all the answers

    What is the order of operations?

    <p>A set of rules that tells the order in which to compute</p> Signup and view all the answers

    What is a variable?

    <p>A symbol used to represent a quantity that can change</p> Signup and view all the answers

    What is a coefficient?

    <p>The number that is multiplied by the variable in an algebraic expression</p> Signup and view all the answers

    What is a term?

    <p>A number, a variable, or the product of a number and a variable</p> Signup and view all the answers

    No less than means ___

    Signup and view all the answers

    Fewer than means ___

    Signup and view all the answers

    At least means ___

    Signup and view all the answers

    Study Notes

    Key Algebra Concepts

    • Constant: A value that remains unchanged throughout a mathematical context.
    • Inequality: A mathematical expression that signifies the comparison of two quantities.
    • Solution of an Inequality: A specific value that satisfies the conditions of the inequality.
    • Solution Set: The complete collection of all possible solutions for a particular inequality.
    • Graph of an Inequality: Visual representation that illustrates the solution set on a number line.

    Graphical Representations

    • Open Circle: Represents a point that is excluded from the solution on a number line.
    • Closed Circle: Indicates a point that is included in the solution on a number line.

    Properties of Equality

    • Properties of Equality: Principle stating that operations performed on one side of an equation must be reflected on the other side.
    • Change the Direction of the Sign: Multiplying or dividing both sides of an inequality by a negative number flips the inequality sign.

    Types of Inequalities

    • Compound Inequality: Combination of two inequalities connected by "and" or "or".
    • Greater Than: Refers to all values exceeding a specified number.
    • Less Than: Pertains to values that fall below a given number.
    • Greater Than or Equal To: Encompasses numbers larger than or exactly equal to a specified value.
    • Less Than or Equal To: Covers numbers smaller than or equal to a certain value.

    Equations and Expressions

    • Equation: A mathematical expression that equates two sides, featuring an equals sign.
    • Expression: A collection of numbers, variables, and operations without an equals sign.

    Number Types

    • Integer: Whole numbers that include positive numbers, negative numbers, and zero.
    • Consecutive Integers: Integers that follow in sequence, such as 1, 2, 3.
    • Whole Numbers: Non-negative integers including zero.
    • Natural Numbers: Counting numbers starting from 1 and incrementing positively.
    • Rational Numbers: Values expressed as a ratio of integers, with a non-zero denominator.
    • Irrational Numbers: Numbers that cannot be represented as ratios of integers.
    • Real Numbers: All numbers comprising both rational and irrational types.

    Algebraic Principles

    • Addition Property of Equality: Adding the same value to both sides of an equation preserves equality.
    • Subtraction Property of Equality: Subtracting the same value from both sides keeps the equation balanced.
    • Multiplication Property of Equality: Multiplying both sides by the same number retains equality.
    • Division Property of Equality: Dividing both sides by the same non-zero number maintains equality.
    • Substitution Property of Equality: Allows for the replacement of an equal value without altering the equation.
    • Distributive Property: States that multiplying a number by a sum is equivalent to summing the products of each addend.

    Additional Vocabulary

    • Variable: A symbol representing a quantity that can vary or change.
    • Coefficient: A numerical factor that multiplies a variable in an algebraic expression.
    • Term: An individual component of an algebraic expression, which can be a number, variable, or combination of both.
    • Order of Operations: Prescribed sequence for performing calculations to ensure consistent results.
    • Infinitely Many Solutions: Indicates that any value for the variable qualifies as a solution to the equation.
    • No Solution: Suggests that there exists no possible number that can satisfy the equation.

    Important Inequality Terms

    • No Less Than: A phrase indicating a minimum threshold to be met.
    • Fewer Than: Implies a restriction that is strictly less than a specified amount.
    • At Least: Signifies a lower boundary that must be met or exceeded.

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    Description

    Test your knowledge of fundamental algebra concepts including constants, inequalities, and their graphical representations. This quiz also explores properties of equality and how they impact solutions of inequalities. Strengthen your understanding of algebraic expressions and their notations.

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