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

Question

(3x−8)+(2x+5)−(4x−8)

(3 points)
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

x−13+8
x minus 13 plus 8

x−21
x minus 21

x+5

Answer 1

Let's simplify the original expression step by step.

The original expression is: \[ (3x - 8) + (2x + 5) - (4x - 8) \]

1. First, distribute the negative sign across the third term: \[ (3x - 8) + (2x + 5) - 4x + 8 \]

2. Next, combine the like terms: \[ (3x + 2x - 4x) + (-8 + 5 + 8) \]

3. Simplifying the \( x \) terms: \[ 3x + 2x - 4x = (3 + 2 - 4)x = 1x = x \]

4. Now simplify the constant terms: \[ -8 + 5 + 8 = -8 + (5 + 8) = -8 + 13 = 5 \]

So, the original expression simplifies to: \[ x + 5 \]

Now, let's determine which of the provided responses are equivalent to \( x + 5 \).

1. \( 3x - 8 + 2x + 5 - 4x - 8 \): This is equivalent to the original expression. \( ⇒ x + 5 \) (true).
2. \( 3x - 8 + 2x + 5 - 4x + 8 \) : This would lead to \( (3 + 2 - 4)x + (-8 + 5 + 8) = x + 5 \) (true).
3. \( 3x + 2x - 4x - 8 + 5 + 8 \): This simplifies to \( x + 5 \) (true).
4. \( x - 13 + 8 \): This simplifies to \( x - 5 \) (not equivalent).
5. \( x - 21 \): This is not equivalent (not equivalent).
6. \( x + 5 \): This is equivalent.

Thus, the equivalent expressions are:

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

Answer 2

a b c or d