Ask a New Question
Menu

Consider this equation and the steps taken to solve it.

 –9(a – 5) = –18  (distribute)

 –9a + 45 = –18  (subtract 45)

    –9a = –63  (divide by –9)

    a = 7

What steps might you take to verify the solution? Check all that apply.
Substitute 7 for a.
Pick any value for a and substitute.
Simplify the equation after substituting the value for a.
Verify that a = 7 is correct when the result is a true statement.
Verify that a = 7 is correct when the result is a false statement.

1 answer

To verify the solution \( a = 7 \) for the equation \( -9(a - 5) = -18 \), you can take the following steps:

  1. Substitute 7 for a: This involves replacing \( a \) with 7 in the original equation to see if both sides of the equation equal each other.

  2. Simplify the equation after substituting the value for a: After substituting \( a = 7 \), simplify both sides of the equation to check for equality.

  3. Verify that a = 7 is correct when the result is a true statement: If substituting 7 into the equation results in a true statement (e.g., both sides of the equation are equal), then you have verified that \( a = 7 \) is indeed the correct solution.

The following steps would not be appropriate for verifying the solution:

  • Pick any value for a and substitute: This does not help verify if the specific solution \( a = 7 \) is correct.

  • Verify that a = 7 is correct when the result is a false statement: This contradicts the process of verification; a correct solution must yield a true statement.

In summary, the correct steps to verify the solution are:

  • Substitute 7 for a.
  • Simplify the equation after substituting the value for a.
  • Verify that \( a = 7 \) is correct when the result is a true statement.