Which expression is not equivalent to the other three?(1 point)

Question

Responses

−2+5x+2x−4
negative 2 plus 5 x plus 2 x minus 4

4+7x−2
4 plus 7 x minus 2

2x+2+2x+3x−8
2 x plus 2 plus 2 x plus 3 x minus 8

8x−x−6

Answer 1

To determine which expression is not equivalent to the others, we will simplify each expression step by step.

1. Expression 1: −2 + 5x + 2x − 4

   • Combine like terms: \[ = (5x + 2x) + (-2 - 4) = 7x - 6 \]

2. Expression 2: 4 + 7x − 2

   • Combine like terms: \[ = 4 - 2 + 7x = 2 + 7x \]

3. Expression 3: 2x + 2 + 2x + 3x − 8

   • Combine like terms: \[ = (2x + 2x + 3x) + (2 - 8) = 7x - 6 \]

4. Expression 4: 8x − x − 6

   • Combine like terms: \[ = (8x - x) - 6 = 7x - 6 \]

Next, let’s summarize the results:

• Expression 1 simplifies to \(7x - 6\).
• Expression 2 simplifies to \(2 + 7x\) (which is equivalent to \(7x + 2\)).
• Expression 3 simplifies to \(7x - 6\).
• Expression 4 simplifies to \(7x - 6\).

The expression that is different is Expression 2: 4 + 7x − 2, which simplifies to \(2 + 7x\) (or \(7x + 2\)), while the other three expressions simplify to \(7x - 6\).

Thus, the expression that is not equivalent to the other three is: 4 + 7x − 2.