Question

which expressions are equal to this one:
(3x-8)+(2x+5)-(4x-8)
choose all options.
a. 3x-8+2x+5-4x-8
b. 3x-8+2x+5-4x+8
c. 3x+2x-4x-8+5+8
d. x-13+8
e. x-21
f. x=5
i think a, c, e are correct

Answer 1

Let's simplify the original expression step by step and check which of the provided options are equivalent.

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

1. Distribute the negative sign across the last term:
\[
(3x - 8) + (2x + 5) - 4x + 8
\]

2. Combine like terms:
- Combine all \(x\) terms: \(3x + 2x - 4x = (3 + 2 - 4)x = x\)
- Combine constant terms: \(-8 + 5 + 8 = -8 + 5 + 8 = -8 + 13 = 5\)

So the simplified expression is:
\[
x + 5
\]

Now let's evaluate each option to see which ones are equal to \(x + 5\):

**a)** \(3x - 8 + 2x + 5 - 4x - 8\)

Combine like terms:
- \(3x + 2x - 4x = x\)
- \(-8 + 5 - 8 = -11\)

This simplifies to:
\[
x - 11 \quad \text{(Not equal to \(x + 5\))}
\]

**b)** \(3x - 8 + 2x + 5 - 4x + 8\)

Combine like terms:
- \(3x + 2x - 4x = x\)
- \(-8 + 5 + 8 = 5\)

This simplifies to:
\[
x + 5 \quad \text{(Equal to \(x + 5\))}
\]

**c)** \(3x + 2x - 4x - 8 + 5 + 8\)

Combine like terms:
- \(3x + 2x - 4x = x\)
- \(-8 + 5 + 8 = 5\)

This simplifies to:
\[
x + 5 \quad \text{(Equal to \(x + 5\))}
\]

**d)** \(x - 13 + 8\)

Combine like terms:
- \(-13 + 8 = -5\)

This simplifies to:
\[
x - 5 \quad \text{(Not equal to \(x + 5\))}
\]

**e)** \(x - 21\)

This is not equal to \(x + 5\).

**f)** \(x = 5\)

This is an equation, not a numerical expression to compare.

Based on this analysis, the correct options that simplify to the original expression \(x + 5\) are:

- **b**: \(3x - 8 + 2x + 5 - 4x + 8\)
- **c**: \(3x + 2x - 4x - 8 + 5 + 8\)

Therefore, the correct options are **b** and **c**. Options **a**, **d**, **e**, and **f** are not equivalent to the original expression.