Question

Which of the following expressions are not equivalent to the expression 2x + 2 - 5x + 7 - 3? Select all that apply.

A: 2x + 11 - 5x
B: -3x + 6
C: 3x - 6
D: 2(x + 1)- 5x + 4
E: 2(x + 1)- (5/2)x + 2

Answer 1

Not equivalent expressions choices are:

• A: 2x + 11 - 5x
• C: 3x - 6
• E: 2(x + 1)- (5/2)x + 2

Explanation:

Let's simplify the expression 2x + 2 - 5x + 7 - 3 term by term.

`\sf 2x + 2 - 5x + 7 - 3 = (2x - 5x) + (2 + 7 - 3) = -3x + 6`

Now, let's compare the simplified expression, -3x + 6, to the answer choices.

• 
  `\sf A: 2x + 11 - 5x = (2x - 5x) + 11 = -3x + 11.`
  This is not equivalent to the original expression.

• 
  `\sf B: -3x + 6.`
  This is equivalent to the simplified expression.

• 
  `\sf C: 3x - 6.`
  This is not equivalent to the simplified expression.

• 
  `\sf D: 2(x + 1)- 5x + 4 = 2x + 2 - 5x + 4 = -3x + 6.`
  This is equivalent to the simplified expression.

• 
  `\sf E: 2(x + 1)-\left ((5)/(2)\right)x + 2 = 2x + 2 -\left ((5)/(2)\right)x + 2 \\= \left (4-(5)/(2)\right)x + 4 =\left((4*2 -5 )/(2)\right) x+4\\=\left((3)/(2)\right)x +4`
  This is not equivalent to the simplified expression.

Therefore, the answer choices that are not equivalent to the expression 2x + 2 - 5x + 7 - 3 are A, C, and E