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Questions and Answers
What is a variable?
What is a variable?
Symbol for an unknown value.
Provide an example of a variable.
Provide an example of a variable.
a + 1 = x; a and x are variables.
What is an algebraic expression?
What is an algebraic expression?
A set of terms that represent a value but no equal sign.
What is the difference between an equation and an expression?
What is the difference between an equation and an expression?
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What is an equation?
What is an equation?
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What is a dependent variable?
What is a dependent variable?
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The dependent variable is usually on which axis?
The dependent variable is usually on which axis?
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What is an independent variable?
What is an independent variable?
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The independent variable is usually on which axis?
The independent variable is usually on which axis?
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Provide an example of independent and dependent variables.
Provide an example of independent and dependent variables.
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What can you do to terms with the same variable in an equation?
What can you do to terms with the same variable in an equation?
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What should you do to parentheses before combining like terms?
What should you do to parentheses before combining like terms?
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What is an equivalent expression?
What is an equivalent expression?
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What is a linear equation?
What is a linear equation?
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What happens when you divide by 0?
What happens when you divide by 0?
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What is a true equation?
What is a true equation?
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What is an algebraic equation?
What is an algebraic equation?
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How do you get rid of a variable on one side of the equation?
How do you get rid of a variable on one side of the equation?
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What is the inverse of multiplication?
What is the inverse of multiplication?
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What is the inverse of addition?
What is the inverse of addition?
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When does an algebraic equation have only one solution?
When does an algebraic equation have only one solution?
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When does an equation have zero solutions?
When does an equation have zero solutions?
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When does an equation have infinite solutions?
When does an equation have infinite solutions?
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What is the sum of consecutive odd or even integers?
What is the sum of consecutive odd or even integers?
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What is a unit rate?
What is a unit rate?
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How do you set up a unit rate?
How do you set up a unit rate?
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When multiplying or dividing inequalities by a negative, what happens to the inequality sign?
When multiplying or dividing inequalities by a negative, what happens to the inequality sign?
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Study Notes
Variables
- A variable is a symbol representing an unknown value.
- Examples of variables include letters like a and x in the expression a + 1 = x.
Algebraic Expressions and Equations
- An algebraic expression consists of terms but lacks an equal sign, such as 3x + 2.
- An equation represents a statement that two expressions are equal, demonstrated as 2x + 1 = 5.
Dependent and Independent Variables
- A dependent variable is measured and typically plotted on the y-axis.
- An independent variable is manipulated and is usually placed on the x-axis.
- For instance, in the scenario where John works x hours at $3 per hour, his total earnings y are dependent on x, resulting in the equation 3x = y.
Combining Like Terms
- Terms with the same variable can be combined to simplify expressions, e.g., 2x + 3y - 2x simplifies to 1x + 3y.
- Proper distribution of parentheses is required before combining, such as turning 2x(3x + 25) into 6x² + 48x.
Equivalent Expressions
- Equivalent expressions represent the same value regardless of their form, e.g., 4a + 8 is equivalent to 2(2a + 4).
Types of Equations
- A linear equation has its highest power as 1, exemplified by 2x + 2.
- Dividing by zero results in an undefined scenario within mathematics.
Solutions to Equations
- An equation has one solution when a variable equals a specific number, such as x = 5.
- An equation has zero solutions when conflicting values exist on both sides, like 4 = 6.
- An equation has infinite solutions when both sides are identically equal, e.g., 13 = 13.
Integer Relationships
- The sum of consecutive odd or even integers can be expressed with x, x + 2, x + 4 to capture the relationship between integers.
Unit Rates
- A unit rate is defined as a rate whose denominator is one, essential for comparing quantities.
- Setting up a unit rate involves dividing the dependent variable by the independent variable, such as distance per hour based on a speed, exemplified by 45 m/hr.
Inequalities
- When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be flipped. For example, -2x > 4 would change the inequality if isolating x.
Studying That Suits You
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Description
Test your understanding of key algebra concepts with these flashcards. From definitions of variables to distinctions between equations and expressions, this quiz covers essential terms and their meanings. Perfect for brushing up on algebra basics!