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

Let's simplify the given expression step by step and then determine which of the options are equivalent to it.

The expression given is:

\[ (3x - 8) + (2x + 5) - (4x - 8) \]

First, simplify the expression:

1. Remove the parentheses:

\[ 3x - 8 + 2x + 5 - 4x + 8 \]

2. Combine like terms:

• For the \(x\) terms: \(3x + 2x - 4x = (3 + 2 - 4)x = 1x = x\)
• For the constant terms: \(-8 + 5 + 8 = (-8 + 8) + 5 = 0 + 5 = 5\)

So the simplified expression is:

\[ x + 5 \]

Now, let's evaluate each of the responses to see which ones are equivalent to \(x + 5\):

1. \(3x−8+2x+5−4x−8\):

   • Simplifies to \(x + 5\) (equivalent).

2. \(3x−8+2x+5−4x+8\):

   • Simplifies to \(x - 8 + 5 + 8 = x + 5\) (equivalent).

3. \(3x + 2x - 4x - 8 + 5 + 8\):

   • Simplifies to \(x - 8 + 5 + 8 = x + 5\) (equivalent).

4. \(5x−4x−8+5+8\):

   • Simplifies to \(x - 8 + 5 + 8 = x + 5\) (equivalent).

5. \(x−8+5+8\):

   • Simplifies to \(x - 8 + 5 + 8 = x + 5\) (equivalent).

6. \(x−13+8\):

   • Simplifies to \(x - 5\) (not equivalent).

7. \(x−3+8\):

   • Simplifies to \(x + 5\) (equivalent).

8. \(x−21\):

   • Simplifies to \(x - 21\) (not equivalent).

9. \(x+5\):

   • This is directly \(x + 5\) (equivalent).

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

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

These are the equivalent expressions.

Answer 2

you can only choose 6

Answer 3

Got it! Let's identify only six responses from the version we have simplified that are equivalent to \(x + 5\):

1. \(3x−8+2x+5−4x−8\): Simplifies to \(x + 5\).
2. \(3x−8+2x+5−4x+8\): Simplifies to \(x + 5\).
3. \(3x + 2x - 4x - 8 + 5 + 8\): Simplifies to \(x + 5\).
4. \(5x−4x−8+5+8\): Simplifies to \(x + 5\).
5. \(x−8+5+8\): Simplifies to \(x + 5\).
6. \(x−3+8\): Simplifies to \(x + 5\).

Since \(x + 5\) is already included, you might want to replace another choice with \(x + 5\) as it directly states the equivalent expression.

So the final selection of six expressions that are equivalent to the initial expression is:

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

Let me know if you need me to adjust anything further!