Question
When solving an equation, Carmen's first step is shown below. Which property justifies Carmen's first step?
Original Equation: 16−4x=16
First Step:x=−4
Original Equation: 16−4x=16
First Step:x=−4
Answers
Answered by
GPT-4o mini
To justify Carmen's first step in solving the equation \( 16 - 4x = 16 \) and arriving at \( x = -4 \), we need to examine the manipulation involved.
1. First, Carmen subtracts \( 16 \) from both sides of the equation:
\[
16 - 4x - 16 = 16 - 16
\]
This simplifies to:
\[
-4x = 0
\]
2. Next, Carmen divides both sides by \( -4 \):
\[
x = \frac{0}{-4}
\]
This results in:
\[
x = 0
\]
However, the equation \( 16 - 4x = 16 \) actually needs revision, as the only solution derived from what is provided doesn’t arrive at \( x = -4 \).
To actually attain \( x = -4 \), we might consider if there was a miscommunication around the original equation or the computation itself. Should it be \( 16 - 4x = 0 \) instead, solving leads directly to \( x = 4 \).
If Carmen began unchecked and comes to directly specify \( 16 - 4x = 16 \) does not result in having derived correctly \( x = -4 \), real computational checks would be how her property use may need to rely on adjusting through \( 0 \) checks.
To summarize: Carmen's first step involved applying the **Subtraction Property of Equality**, followed by the **Division Property of Equality**.
If indeed error should see something intended and \( x \neq -4 \), look to appropriate functional applications as captured across property usage.
1. First, Carmen subtracts \( 16 \) from both sides of the equation:
\[
16 - 4x - 16 = 16 - 16
\]
This simplifies to:
\[
-4x = 0
\]
2. Next, Carmen divides both sides by \( -4 \):
\[
x = \frac{0}{-4}
\]
This results in:
\[
x = 0
\]
However, the equation \( 16 - 4x = 16 \) actually needs revision, as the only solution derived from what is provided doesn’t arrive at \( x = -4 \).
To actually attain \( x = -4 \), we might consider if there was a miscommunication around the original equation or the computation itself. Should it be \( 16 - 4x = 0 \) instead, solving leads directly to \( x = 4 \).
If Carmen began unchecked and comes to directly specify \( 16 - 4x = 16 \) does not result in having derived correctly \( x = -4 \), real computational checks would be how her property use may need to rely on adjusting through \( 0 \) checks.
To summarize: Carmen's first step involved applying the **Subtraction Property of Equality**, followed by the **Division Property of Equality**.
If indeed error should see something intended and \( x \neq -4 \), look to appropriate functional applications as captured across property usage.
Answer
so whats the answer
Answered by
GPT-4o mini
To clarify the answer regarding Carmen's first step in solving the equation \(16 - 4x = 16\):
1. **Subtraction Property of Equality**: Carmen first subtracts \(16\) from both sides, which is justified by the Subtraction Property of Equality.
The equation becomes:
\[
16 - 4x - 16 = 16 - 16
\]
This simplifies to:
\[
-4x = 0
\]
2. Then, to solve for \(x\), she would divide both sides by \(-4\), which is justified by the **Division Property of Equality**.
In short, Carmen's first step can be justified by the **Subtraction Property of Equality**.
1. **Subtraction Property of Equality**: Carmen first subtracts \(16\) from both sides, which is justified by the Subtraction Property of Equality.
The equation becomes:
\[
16 - 4x - 16 = 16 - 16
\]
This simplifies to:
\[
-4x = 0
\]
2. Then, to solve for \(x\), she would divide both sides by \(-4\), which is justified by the **Division Property of Equality**.
In short, Carmen's first step can be justified by the **Subtraction Property of Equality**.