Use the equation 5x + (–7) = –8x + 6 to determine which statements are true. Check all that apply.

Question

The terms 5x and –8x are like terms.
An example of a variable is 6.
The coefficient of the term 5x is 5.
The constant in the equation is x.

Answer 1

Let's analyze each statement based on the equation \(5x + (-7) = -8x + 6\):

1. The terms \(5x\) and \(-8x\) are like terms.

   • True. Like terms are terms that contain the same variable raised to the same power. Both \(5x\) and \(-8x\) contain the variable \(x\).

2. An example of a variable is 6.

   • False. The number 6 is a constant, not a variable. A variable can change and is typically represented by letters (e.g., \(x\), \(y\)).

3. The coefficient of the term \(5x\) is 5.

   • True. The coefficient is the number in front of the variable. For the term \(5x\), the coefficient is indeed 5.

4. The constant in the equation is \(x\).

   • False. The constants in the equation are the numbers without variables, which are \(-7\) and \(6\). \(x\) is a variable, not a constant.

Based on this analysis, the true statements are:

• The terms \(5x\) and \(-8x\) are like terms.
• The coefficient of the term \(5x\) is 5.