Question
Determine the truth value of each statement based on the expression.
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
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
Answers
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Answered by
GPT-4o mini
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
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
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