Determine the truth value of each statement based on the expression.

Question

6x 2 - 2x - 14y + 3x

1. Before simplifying, there are 4 terms in the expression.

2. 6x2 and 3x are like terms.

3. The coefficient on y is 14.

4. Simplified, the expression is 6x 2 + 5x - 14y.

5. The commutative property allows the expression to be written as 6x 2 - 14y + 3x - 2x.

true or false for every one

Answer 1

Let's analyze each statement based on the expression \( 6x^2 - 2x - 14y + 3x \).

1. Before simplifying, there are 4 terms in the expression.

   • The expression can be broken down into four parts: \( 6x^2 \), \( -2x \), \( -14y \), and \( 3x \).
   • True.

2. 6x² and 3x are like terms.

   • Like terms are terms that have the same variable raised to the same power. \( 6x^2 \) and \( 3x \) have different powers (\( x^2 \) and \( x^1 \)), so they are not like terms.
   • False.

3. The coefficient on y is 14.

   • The term \( -14y \) means that the coefficient of \( y \) is \(-14\), not \( 14\).
   • False.

4. Simplified, the expression is 6x² + 5x - 14y.

   • When simplifying, we combine like terms. The like terms in the expression are \( -2x \) and \( 3x \), which combine to make \( 5x \). Therefore, the expression simplifies to \( 6x^2 + 5x - 14y \).
   • True.

5. The commutative property allows the expression to be written as 6x² - 14y + 3x - 2x.

   • The commutative property states that the order of addition does not change the sum. The terms \( 6x^2 \), \( -14y \), \( 3x \), and \( -2x \) can indeed be rearranged this way without changing the expression.
   • True.

In summary, the truth values for the statements are:

1. True
2. False
3. False
4. True
5. True