Identifying Equivalent Expressions Flashcard

Front

What is an equivalent expression?

Back

An equivalent expression is an expression that has the same value as another expression for all values of the variables involved.

Front

How do you simplify the expression 5x + 2y - 3x + 4y?

Back

Combine like terms: (5x - 3x) + (2y + 4y) = 2x + 6y.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across terms inside parentheses.

Front

How do you apply the distributive property to the expression 3(2x - 4)?

Back

Using the distributive property: 3 * 2x - 3 * 4 = 6x - 12.

Front

What does it mean to check if two expressions are equivalent?

Back

To check if two expressions are equivalent, substitute the same values for the variables in both expressions and see if they yield the same result.

Front

What is the result of substituting x = 2 and y = 3 into the expressions 2x + 3y and 5x - 2y?

Back

For 2x + 3y: 2(2) + 3(3) = 4 + 9 = 13. For 5x - 2y: 5(2) - 2(3) = 10 - 6 = 4. They are not equivalent.

Front

How do you combine like terms in an expression?

Back

Combine terms that have the same variable raised to the same power by adding or subtracting their coefficients.

Front

What is the simplified form of the expression 2(3x - 4) - 5?

Back

Distributing gives 6x - 8 - 5, which simplifies to 6x - 13.

Front

What are like terms?

Back

Like terms are terms in an expression that have the same variable raised to the same power.

Front

What is the first step in simplifying an expression?

Back

Identify and combine like terms.