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Which of the following statements about the equation 2x−5=8+x is correct?

Statement #1: There are two constants in the equation.

Statement #2: x does not have a coefficient.

Statement #3: There are two terms in the equation.

Statement #$$ is correct.

1 answer

Let's analyze the equation \( 2x - 5 = 8 + x \) to evaluate the statements.

  1. Statement #1: There are two constants in the equation.

    • The constants in the equation are \(-5\) and \(8\). So, this statement is correct.

  2. Statement #2: \(x\) does not have a coefficient.

    • In the equation, \(x\) has a coefficient of \(1\) (implicitly). Therefore, this statement is incorrect.

  3. Statement #3: There are two terms in the equation.

    • The equation has more than two terms because on the left side we have \(2x\) and \(-5\), and on the right side, we have \(8\) and \(x\). So, the whole equation contains four terms. Thus, this statement is incorrect.

From this analysis, only Statement #1 is correct.