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Question
Select the THREE expressions that are equivalent to this algebraic expression.

(3x−8)+(2x+5)−(4x−8)


(3 points)
Responses

x−5
x minus 5

3x+2x−4x−8+5+8
3 x plus 2 x minus 4 x minus 8 plus 5 plus 8

10x−21
10 x minus 21

3x−8+2x+5−4x−8
3 x minus 8 plus 2 x plus 5 minus 4 x minus 8

x+5
x plus 5

x−21
x minus 21

3x−8+2x+5−4x+8
3 x minus 8 plus 2 x plus 5 minus 4 x plus 8
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1 answer

Let's simplify the expression \((3x−8)+(2x+5)−(4x−8)\) step by step first.

  1. Distributing the negative sign: \[ (3x - 8) + (2x + 5) - 4x + 8 \]

  2. Combining like terms:

    • Combine \(3x\), \(2x\), and \(-4x\): \[ 3x + 2x - 4x = (3 + 2 - 4)x = 1x = x \]
    • Combine the constants \(-8\), \(+5\), and \(+8\): \[ -8 + 5 + 8 = (-8 + 5 + 8) = 5 \]

Putting it all together, we have: \[ x + 5 \]

Now, let's find the expressions equivalent to this simplified form \(x + 5\):

  1. \(x - 5\) - Not equivalent.
  2. \(3x + 2x - 4x - 8 + 5 + 8\) - Equivalent since this simplifies to \(x + 5\).
  3. \(10x - 21\) - Not equivalent.
  4. \(3x - 8 + 2x + 5 - 4x - 8\) - Equivalent since this simplifies to \(x + 5\).
  5. \(x + 5\) - Equivalent.
  6. \(x - 21\) - Not equivalent.
  7. \(3x - 8 + 2x + 5 - 4x + 8\) - Equivalent since this simplifies to \(x + 5\).

Therefore, the three expressions that are equivalent to \(x + 5\) are:

  • \(3x + 2x - 4x - 8 + 5 + 8\)
  • \(3x - 8 + 2x + 5 - 4x - 8\)
  • \(x + 5\)

So the correct selections are:

  • \(3x + 2x - 4x - 8 + 5 + 8\)
  • \(3x - 8 + 2x + 5 - 4x - 8\)
  • \(x + 5\)