Question

expressions that are equivalent to this algebraic expression

3x - 80 + (2x + 5) - (4x - 8)

Answer 1

To find expressions equivalent to the algebraic expression \(3x - 80 + (2x + 5) - (4x - 8)\), we can first simplify the given expression step by step.

1. Distribute the negative sign in front of \((4x - 8)\):
\[
3x - 80 + 2x + 5 - 4x + 8
\]

2. Combine like terms:
- For the \(x\) terms: \(3x + 2x - 4x = (3 + 2 - 4)x = 1x = x\)
- For the constant terms: \(-80 + 5 + 8 = -80 + 13 = -67\)

So, the simplified expression is:
\[
x - 67
\]

### Equivalent Expressions
Now we can express this in different equivalent forms. Here are some equivalent expressions to \(x - 67\):

1. **Standard form**:
\[
x - 67
\]

2. **Adding and subtracting the same value**:
\[
x - 70 + 3
\]
(Adding -70 and +3 gives -67)

3. **Factored form** (expressing as a product if possible):
\[
1(x - 67)
\]

4. **Rearranged form**:
\[
-67 + x
\]

5. **Expressing in terms of a different variable**:
\[
y = x - 67 \quad \text{where } y \text{ is another variable}
\]

All these forms maintain the same value as the original expression, thus are equivalent.