Select all of the expressions that are equivalent to this algebraic expression.

Question

(3x−8)+(2x+5)−(4x−8)

(1 point)
Responses

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

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

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

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

x−8+5+8
x minus 8 plus 5 plus 8

x−13+8
x minus 13 plus 8

x−3+8
x minus 3 plus 8

x−21
x minus 21

x+5

Answer 1

To determine which expressions are equivalent to the original algebraic expression \((3x−8)+(2x+5)−(4x−8)\), let's simplify it step by step.

1. Start with the original expression: \[ (3x - 8) + (2x + 5) - (4x - 8) \]

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

3. Combine like terms:

   • Combine \(3x + 2x - 4x\): \[ 3x + 2x - 4x = x \]
   • Combine constants \(-8 + 5 + 8\): \[ -8 + 5 + 8 = -8 + 5 + 8 = -8 + 13 = 5 \]

4. The expression simplifies to: \[ x + 5 \]

Now, let's review the provided responses to identify which expressions are equivalent to \(x + 5\):

1. \(3x−8+2x+5−4x−8\)

   • Equivalent (This simplifies to \(x + 5\) as worked out above).

2. \(3x−8+2x+5−4x+8\)

   • Not Equivalent (This simplifies to \(x + 13\)).

3. \(3x+2x−4x−8+5+8\)

   • Equivalent (This simplifies to \(x + 5\)).

4. \(5x−4x−8+5+8\)

   • Equivalent (This simplifies to \(x + 5\)).

5. \(x−8+5+8\)

   • Equivalent (This simplifies to \(x + 5\)).

6. \(x−13+8\)

   • Not Equivalent (This simplifies to \(x - 5\)).

7. \(x−3+8\)

   • Not Equivalent (This simplifies to \(x + 5\)).

8. \(x−21\)

   • Not Equivalent (This simplifies to \(x - 21\)).

9. \(x+5\)

   • Equivalent (This is exactly what we simplified to).

So, the expressions that are equivalent to the original expression \( (3x−8)+(2x+5)−(4x−8) \) are:

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

Thus, the equivalent expressions are:

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