Which of the following statements about the equation `3x-1=7+x` is correct?

Question

there are 2 constants in the equation
x does not have a coefficient
there are 2 terms in the equation
A coefficient is negative

Answer 1

Let's analyze the equation \( 3x - 1 = 7 + x \).

1. There are 2 constants in the equation:

   • The constants in this equation are \(-1\) and \(7\). Therefore, this statement is correct.

2. x does not have a coefficient:

   • In this equation, the term \(3x\) has a coefficient of \(3\), and the term \(x\) (which can be written as \(1x\)) has a coefficient of \(1\). Thus, this statement is incorrect.

3. There are 2 terms in the equation:

   • The left side \(3x - 1\) has two terms: \(3x\) and \(-1\). The right side \(7 + x\) also has two terms: \(7\) and \(x\). So, in total, there are four terms in the equation. Therefore, this statement is incorrect.

4. A coefficient is negative:

   • The coefficients of the terms in the equation are \(3\) (positive) and \(1\) (also positive). The number \(-1\) is a constant, not a coefficient. Therefore, this statement is incorrect.

In conclusion, the correct statement is: there are 2 constants in the equation.