Khan Academy Algebra Flashcards

Questions and Answers

What is a variable?

Symbol for an unknown value.

Provide an example of a variable.

a + 1 = x; a and x are variables.

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?

Equation: relation sign (like = or >); Expression: no relation sign. Signup and view all the answers

What is an equation?

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

What is a dependent variable?

Variable that is measured. Signup and view all the answers

The dependent variable is usually on which axis?

Y-axis. Signup and view all the answers

What is an independent variable?

Variable that is manipulated. Signup and view all the answers

The independent variable is usually on which axis?

X-axis. Signup and view all the answers

Provide an example of independent and dependent variables.

John works x hours and makes $3 per hour. Total in y after x hours is 3x = y. Signup and view all the answers

What can you do to terms with the same variable in an equation?

Combine them. Signup and view all the answers

What should you do to parentheses before combining like terms?

Distribute the parentheses properly. Signup and view all the answers

What is an equivalent expression?

Expressions that represent the same value. Signup and view all the answers

What is a linear equation?

Algebraic expression where the highest power is 1. Signup and view all the answers

What happens when you divide by 0?

Undefined. Signup and view all the answers

What is a true equation?

Expressions on both sides of the equal sign are equal. Signup and view all the answers

What is an algebraic equation?

An expression with one or more variables. Signup and view all the answers

How do you get rid of a variable on one side of the equation?

Do the opposite operation on both sides that cancels it out. Signup and view all the answers

What is the inverse of multiplication?

Division. Signup and view all the answers

What is the inverse of addition?

Subtraction. Signup and view all the answers

When does an algebraic equation have only one solution?

If there is one number equaling a variable. Signup and view all the answers

When does an equation have zero solutions?

When there are two different values on each side of the equal sign. Signup and view all the answers

When does an equation have infinite solutions?

When both sides of the equation have equal numerical values. Signup and view all the answers

What is the sum of consecutive odd or even integers?

Set up as x, x+2, x+4. Signup and view all the answers

What is a unit rate?

A rate with a denominator of 1. Signup and view all the answers

How do you set up a unit rate?

Dependent variable/independent variable. Signup and view all the answers

When multiplying or dividing inequalities by a negative, what happens to the inequality sign?

Flip it. Signup and view all the answers

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.

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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!