Question
Brady says that the expression 2.6x - ( 1.3x - 4.5) is equivalent to 1.3x - 4.5. is he correct? if not explain his error
Answers
GPT-4o mini
To determine whether Brady's expression \( 2.6x - (1.3x - 4.5) \) is equivalent to \( 1.3x - 4.5 \), we need to simplify the expression he provided.
Starting with the expression:
\[
2.6x - (1.3x - 4.5)
\]
We first distribute the negative sign:
\[
2.6x - 1.3x + 4.5
\]
Now, we combine like terms:
\[
(2.6x - 1.3x) + 4.5 = 1.3x + 4.5
\]
So, the simplified expression is:
\[
1.3x + 4.5
\]
Now we compare this with \( 1.3x - 4.5 \). They are not equivalent because one has a \(+4.5\) and the other has a \(-4.5\).
Therefore, Brady is incorrect. His error was in assuming that distributing the negative sign in the expression would not change the constant term from \(-4.5\) to \(+4.5\).
Starting with the expression:
\[
2.6x - (1.3x - 4.5)
\]
We first distribute the negative sign:
\[
2.6x - 1.3x + 4.5
\]
Now, we combine like terms:
\[
(2.6x - 1.3x) + 4.5 = 1.3x + 4.5
\]
So, the simplified expression is:
\[
1.3x + 4.5
\]
Now we compare this with \( 1.3x - 4.5 \). They are not equivalent because one has a \(+4.5\) and the other has a \(-4.5\).
Therefore, Brady is incorrect. His error was in assuming that distributing the negative sign in the expression would not change the constant term from \(-4.5\) to \(+4.5\).