Question

Select all expressions that are equivalent to this algebraic expression
(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.