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

Question

(3x−8)+(2x+5)−(4x−8)

(3 points)
Responses

x−5

3x−8+2x+5−4x+8

3x+2x−4x−8+5+8

3x−8+2x+5−4x−8

x−21

10x−21

x+5

GPT-4o mini · Answer

To simplify the algebraic expression $(3 x - 8) + (2 x + 5) - (4 x - 8)$ , let's break it down step by step:

Remove the parentheses: $3 x - 8 + 2 x + 5 - 4 x + 8$
Combine like terms:
- For the $x$ terms: $3 x + 2 x - 4 x = (3 + 2 - 4) x = 1 x$ or simply $x$ .
- For the constant terms: $- 8 + 5 + 8 = - 8 + 13 = 5$ .

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

Now, we need to evaluate the given responses to see which three are equivalent to the original expression:

$x - 5$ : Not equivalent.
$3 x - 8 + 2 x + 5 - 4 x + 8$ : Equivalent (this is just rewriting the original expression).
$3 x + 2 x - 4 x - 8 + 5 + 8$ : Equivalent (this is another rearrangement of the original expression).
$3 x - 8 + 2 x + 5 - 4 x - 8$ : Equivalent (again, just rewriting the original expression).
$x - 21$ : Not equivalent.
$10 x - 21$ : Not equivalent.
$x + 5$ : Equivalent (this is the simplified version).

The three expressions that are equivalent to the original expression are:

In conclusion, the correct responses are:

$3 x - 8 + 2 x + 5 - 4 x + 8$
$3 x + 2 x - 4 x - 8 + 5 + 8$
$3 x - 8 + 2 x + 5 - 4 x - 8$ (any one of these three rewritten forms could be selected, so depending on your answer options, you can also include $x + 5$ as a final equivalent).