Question

which expression is equivalent to 3x + 2

Answer 1

answer choices

x + x + x + 1 + 1

x + x + 1 + 1 + 1

3x +6

3 + x + 2

Answer 2

The expression \(3x + 2\) can be expressed in several equivalent forms by applying algebraic principles. Here are a few examples:

1. Factored form: You can factor out a common term if applicable; however, this expression isn't easily factored in terms of integers.

2. Adding or subtracting the same value: You could express it by adding and then subtracting 2, for example:
\[
3x + 2 = 3x + 2 - 2 + 2 = 3x + 0
\]

3. In terms of different variables: You can replace \(x\) with another variable, say \(y\) (if you assume \(y = x\)), so:
\[
3y + 2
\]

4. Or by rearranging the terms:
\[
2 + 3x
\]

These are just a few examples of expressions that are equivalent to \(3x + 2\). If you meant to ask for specific forms or other types of equivalent expressions, feel free to clarify!

Answer 3

To determine which expression is equivalent to \(3x + 2\), let’s simplify each of the answer choices given:

1. **Choice 1:** \(x + x + x + 1 + 1\)
Simplifying this:
\[
x + x + x + 1 + 1 = 3x + 2
\]

2. **Choice 2:** \(x + x + 1 + 1 + 1\)
Simplifying this:
\[
x + x + 1 + 1 + 1 = 2x + 3
\]

3. **Choice 3:** \(3x + 6\)
This does not equal \(3x + 2\).

4. **Choice 4:** \(3 + x + 2\)
Simplifying this:
\[
3 + x + 2 = x + 5
\]

Comparing these simplifications to \(3x + 2\), we find that the only equivalent expression is:

**Choice 1:** \(x + x + x + 1 + 1\)

This choice simplifies to \(3x + 2\).