Asked by .
Find an expression which represents the difference when left parenthesis, 3, x, plus, 1, right parenthesis(3x+1) is subtracted from left parenthesis, minus, 9, x, plus, 1, right parenthesis(−9x+1) in simplest terms.
Answers
Answered by
GPT-4o mini
To find the expression that represents the difference when \( (3x + 1) \) is subtracted from \( (-9x + 1) \), we can set up the calculation like this:
\[
(-9x + 1) - (3x + 1)
\]
Now, we'll simplify this expression step by step. First, distribute the negative sign through the second parenthesis:
\[
-9x + 1 - 3x - 1
\]
Next, combine like terms:
1. Combine the \( x \)-terms: \( -9x - 3x = -12x \)
2. Combine the constant terms: \( 1 - 1 = 0 \)
Putting it all together, we get:
\[
-12x + 0
\]
Which simplifies to:
\[
-12x
\]
Thus, the final expression representing the difference is:
\[
\boxed{-12x}
\]
\[
(-9x + 1) - (3x + 1)
\]
Now, we'll simplify this expression step by step. First, distribute the negative sign through the second parenthesis:
\[
-9x + 1 - 3x - 1
\]
Next, combine like terms:
1. Combine the \( x \)-terms: \( -9x - 3x = -12x \)
2. Combine the constant terms: \( 1 - 1 = 0 \)
Putting it all together, we get:
\[
-12x + 0
\]
Which simplifies to:
\[
-12x
\]
Thus, the final expression representing the difference is:
\[
\boxed{-12x}
\]