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

Question

(3x−8)+(2x+5)−(4x−8)


(3 points)
Responses

x+5
x plus 5

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

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

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

x−21
x minus 21

10x−21

Answer 1

To simplify the original expression \((3x−8)+(2x+5)−(4x−8)\), we can follow these steps:

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

2. Combine like terms:

   • Combine the \(x\) terms: \(3x + 2x - 4x = (3 + 2 - 4)x = x\)
   • Combine the constant terms: \(-8 + 5 + 8 = -8 + 5 + 8 = -8 + 13 = 5\)

So the simplified expression is: \[ x + 5 \]

Now we look at the remaining expressions to find which ones are equivalent:

1. \(3x−8+2x+5−4x−8\): This is the same as the original expression written out fully, so it simplifies to \(x + 5\).

2. \(3x−8+2x+5−4x+8\): This has a \(+8\) instead of \(-8\) along with other terms. This leads to \[3x + 2x - 4x - 8 + 5 + 8 = (3 + 2 - 4)x + (-8 + 5 + 8) = x + 5\].

3. \(x−5\): This simplifies to \(x - 5\), which is not equivalent to \(x + 5\).

4. \(x−21\): This simplifies to \(x - 21\), which is not equivalent to \(x + 5\).

5. \(10x−21\): This simplifies to \(10x - 21\), which is not equivalent to \(x + 5\).

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

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

These three answers are:

1. \(x + 5\)
2. \(3x−8+2x+5−4x−8\)
3. \(3x−8+2x+5−4x+8\)