Which expression is equivalent to −3x−5

Question

−
3
𝑥
−
5
?(1 point)
Responses

(x−7)+(2−4x)
(
𝑥
−
7
)
+
(
2
−
4
𝑥
)
left parenthesis x minus 7 right parenthesis plus left parenthesis 2 minus 4 x right parenthesis

−1+(x−4x)+6
−
1
+
(
𝑥
−
4
𝑥
)
+
6
negative 1 plus left parenthesis x minus 4 x right parenthesis plus 6

(−4x−6)+(2+5x)
(
−
4
𝑥
−
6
)
+
(
2
+
5
𝑥
)
left parenthesis negative 4 x minus 6 right parenthesis plus left parenthesis 2 plus 5 x right parenthesis

−1+3x−(2x+6)

Answer 1

To determine which expression is equivalent to \(-3x - 5\), we can simplify each of the given options and see which one matches.

1. Option 1: \((x−7) + (2−4x)\) \[ = x - 7 + 2 - 4x = x - 4x - 7 + 2 = -3x - 5 \] This expression simplifies to \(-3x - 5\).

2. Option 2: \(-1 + (x−4x) + 6\) \[ = -1 + x - 4x + 6 = -1 - 3x + 6 = -3x + 5 \] This expression simplifies to \(-3x + 5\), which is not equivalent.

3. Option 3: \((-4x−6) + (2+5x)\) \[ = -4x - 6 + 2 + 5x = -4x + 5x - 6 + 2 = x - 4 \] This expression simplifies to \(x - 4\), which is not equivalent.

4. Option 4: \(-1 + 3x - (2x + 6)\) \[ = -1 + 3x - 2x - 6 = -1 + 3x - 2x - 6 = 3x - 2x - 1 - 6 = x - 7 \] This expression simplifies to \(x - 7\), which is not equivalent.

The only expression that simplifies to \(-3x - 5\) is Option 1: \((x−7) + (2−4x)\).