Question
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.
–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.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
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.
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