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
x plus 5
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Answer 1

To determine which expressions are equivalent to the algebraic expression $(3x-8)+(2x+5)-(4x-8)$, we first simplify the original expression step by step.

1. Distribute the negative sign in front of $(4x-8)$: $$(3x-8)+(2x+5)-4x+8$$

2. Combine like terms:

   • For the $x$ terms: $3x+2x-4x=1x$ or simply $x$.
   • For the constant terms: $-8+5+8=-8+5+8=-8+13=5$.

So, the simplified expression is: $$x+5$$

Now we can check each of the provided responses to see if they simplify to $x+5$.

1. 3x−8+2x+5−4x−8

   • This simplifies to $3x+2x-4x-8+5-8=x-8+5=x-3$, which is not equivalent.

2. 3x−8+2x+5−4x+8

   • This simplifies to $3x+2x-4x-8+5+8=x+5$, which is equivalent.

3. 3x+2x−4x−8+5+8

   • This also simplifies to $3x+2x-4x-8+5+8=x+5$, which is equivalent.

4. 5x−4x−8+5+8

   • This simplifies to $x-8+5+8=x+5$, which is equivalent.

5. x−8+5+8

   • This simplifies to $x-8+5+8=x+5$, which is equivalent.

6. x−13+8

   • This simplifies to $x-5$, which is not equivalent.

7. x−3+8

   • This simplifies to $x+5$, which is equivalent.

8. x−21

   • This is just $x-21$, which is not equivalent.

9. x+5

   • This is the expression itself, so it is equivalent.

Based on this evaluation, the equivalent expressions are:

• 3x−8+2x+5−4x+8
• 3x+2x−4x−8+5+8
• 5x−4x−8+5+8
• x−8+5+8
• x−3+8
• x+5

So the final equivalent expressions selected are:

• $3x-8+2x+5-4x+8$
• $3x+2x-4x-8+5+8$
• $5x-4x-8+5+8$
• $x-8+5+8$
• $x-3+8$
• $x+5$

Answer 2

a b c or d

Answer 3

Based on the evaluation of the expressions provided, the equivalent options are:

• b) 3x−8 + 2x + 5 − 4x + 8
• c) 3x + 2x − 4x − 8 + 5 + 8
• d) 5x − 4x − 8 + 5 + 8
• e) x − 8 + 5 + 8
• g) x − 3 + 8
• h) x + 5

If I were to narrow it down to just options a, b, c, or d, the correct answers would be:

• b) 3x−8+2x+5−4x+8
• c) 3x+2x−4x−8+5+8
• d) 5x−4x−8+5+8

Thus, the correct options are b, c, and d.