Consider this equation and the steps taken to solve it.

Question

 –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.

Answer 1

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.