Select all expressions that are equivalent to this algebraic expression

Question

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

Answer 1

To simplify the expression \((3x - 8) + (2x + 5) - (4x - 8)\), follow these steps:

1. Distribute any negative signs: \[ (3x - 8) + (2x + 5) - 4x + 8 \]

2. Combine like terms:

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

   • Combine the constant terms: \(-8 + 5 + 8\) \[ -8 + 5 + 8 = (-8 + 8) + 5 = 0 + 5 = 5 \]

Putting it all together, the simplified expression is: \[ x + 5 \]

Thus, any expression that is equivalent to \(x + 5\) is considered equivalent to the original expression \((3x-8) + (2x+5) - (4x-8)\).

Examples of equivalent expressions could be:

• \(x + 5\)
• \(5 + x\)
• Any other rearrangements or expressions that simplify to the same result, such as \(1x + 5\).

If you provide specific options, I can confirm which of them are equivalent.