Asked by daniii
Which expression is equivalent to −3x−5 ?
A, -1+(x-4x)+6
B, (x-7)+(2-4x)
C, (-4x-6)+(2+5x)
D, -1+3x-(2x+6)
A, -1+(x-4x)+6
B, (x-7)+(2-4x)
C, (-4x-6)+(2+5x)
D, -1+3x-(2x+6)
Answers
Answered by
GPT-4o mini
To determine which expression is equivalent to \(-3x - 5\), we need to simplify each option and compare it to \(-3x - 5\).
**Option A:**
\[
-1 + (x - 4x) + 6 = -1 + (-3x) + 6 = -3x + 5
\]
**Option B:**
\[
(x - 7) + (2 - 4x) = x - 7 + 2 - 4x = -3x - 5
\]
**Option C:**
\[
(-4x - 6) + (2 + 5x) = -4x - 6 + 2 + 5x = (5x - 4x) + (-6 + 2) = x - 4
\]
**Option D:**
\[
-1 + 3x - (2x + 6) = -1 + 3x - 2x - 6 = (3x - 2x) + (-1 - 6) = x - 7
\]
Now comparing the simplified expressions:
- A simplifies to \(-3x + 5\)
- B simplifies to \(-3x - 5\) (this is equivalent to our original expression)
- C simplifies to \(x - 4\)
- D simplifies to \(x - 7\)
The expression which is equivalent to \(-3x - 5\) is **Option B**.
**Option A:**
\[
-1 + (x - 4x) + 6 = -1 + (-3x) + 6 = -3x + 5
\]
**Option B:**
\[
(x - 7) + (2 - 4x) = x - 7 + 2 - 4x = -3x - 5
\]
**Option C:**
\[
(-4x - 6) + (2 + 5x) = -4x - 6 + 2 + 5x = (5x - 4x) + (-6 + 2) = x - 4
\]
**Option D:**
\[
-1 + 3x - (2x + 6) = -1 + 3x - 2x - 6 = (3x - 2x) + (-1 - 6) = x - 7
\]
Now comparing the simplified expressions:
- A simplifies to \(-3x + 5\)
- B simplifies to \(-3x - 5\) (this is equivalent to our original expression)
- C simplifies to \(x - 4\)
- D simplifies to \(x - 7\)
The expression which is equivalent to \(-3x - 5\) is **Option B**.
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