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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.

1 answer

Let's analyze each statement about the equation \( 2x - 5 = 8 + x \):

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

    • In the equation, the constants are the numbers that do not contain a variable. The constants in the equation are \(-5\) and \(8\). So there are indeed two constants in the equation. This statement is correct.

  2. Statement #2: x does not have a coefficient.

    • The term involving \(x\) on the left is \(2x\), which has a coefficient of \(2\). The term involving \(x\) on the right is \(x\), which can be understood as having a coefficient of \(1\). Therefore, \(x\) does have a coefficient. This statement is incorrect.

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

    • An equation can have multiple terms on either side. The left side \(2x - 5\) has two terms: \(2x\) and \(-5\) and the right side \(8 + x\) also has two terms: \(8\) and \(x\). So in total, the equation has four terms. This statement is incorrect.

In summary:

  • Statement #1 is correct.
  • Statement #2 is incorrect.
  • Statement #3 is incorrect.

Therefore, the correct statement is Statement #1.