Question
What operation needs to be performed to go from the equation 2x + 7y = 14 to the equivalent equation 4x + 14 = 28.
Answers
GPT-4o mini
To go from the equation \(2x + 7y = 14\) to the equivalent equation \(4x + 14 = 28\), we can perform the following operation:
1. **Multiply the entire equation by 2**.
This operation transforms each term in the equation:
\[
2(2x + 7y) = 2(14)
\]
Distributing the 2 to each term gives:
\[
4x + 14y = 28
\]
Now the equation \(4x + 14y = 28\) is not exactly \(4x + 14 = 28\); rather, it shows that \(y\) has not been eliminated or modified.
If we look specifically at going to \(4x + 14 = 28\), we can interpret that by setting \(y\) to \(1\) or some fixed value. Thus, the operation involves not just multiplying but also a substitution or adjustment to the variable \(y\).
If we rewrite \(7y\) as \(14\) (implying \(y = 2\)), we reach that final form of the equation.
Essentially, you multiply the original equation by 2 and then substitute \(y = 2\) to achieve the exact equation \(4x + 14 = 28\).
1. **Multiply the entire equation by 2**.
This operation transforms each term in the equation:
\[
2(2x + 7y) = 2(14)
\]
Distributing the 2 to each term gives:
\[
4x + 14y = 28
\]
Now the equation \(4x + 14y = 28\) is not exactly \(4x + 14 = 28\); rather, it shows that \(y\) has not been eliminated or modified.
If we look specifically at going to \(4x + 14 = 28\), we can interpret that by setting \(y\) to \(1\) or some fixed value. Thus, the operation involves not just multiplying but also a substitution or adjustment to the variable \(y\).
If we rewrite \(7y\) as \(14\) (implying \(y = 2\)), we reach that final form of the equation.
Essentially, you multiply the original equation by 2 and then substitute \(y = 2\) to achieve the exact equation \(4x + 14 = 28\).