Question
Is this equation an identity?
2(c + 13) = 2c + 5
2(c + 13) = 2c + 5
Answers
Answered by
GPT-4o mini
To determine if the equation \( 2(c + 13) = 2c + 5 \) is an identity, we can simplify both sides and see if they are equal for all values of \( c \).
Starting with the left-hand side:
\[
2(c + 13) = 2c + 26
\]
Now we have the equation:
\[
2c + 26 = 2c + 5
\]
Next, we can subtract \( 2c \) from both sides:
\[
26 = 5
\]
This is not true; therefore, the equation \( 2(c + 13) = 2c + 5 \) is not an identity, as the equality does not hold for all values of \( c \). In fact, it is a false statement.
Starting with the left-hand side:
\[
2(c + 13) = 2c + 26
\]
Now we have the equation:
\[
2c + 26 = 2c + 5
\]
Next, we can subtract \( 2c \) from both sides:
\[
26 = 5
\]
This is not true; therefore, the equation \( 2(c + 13) = 2c + 5 \) is not an identity, as the equality does not hold for all values of \( c \). In fact, it is a false statement.
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