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Let's simplify the given expression in the problem:

The expression is:

\[
12x - 3 + 2x + 13
\]

First, combine the like terms:
- Combine \(12x\) and \(2x\), which gives \(14x\).
- Combine \(-3\) and \(13\), which gives \(+10\).

So, the simplified form of the expression is:

\[
14x + 10
\]

Now, let's check which of the options match this result:

1. \(17x + 13\) — **Not equivalent**.
2. \(14x + 10\) — **Equivalent**.
3. \(14x + 16\) — **Not equivalent**.
4. \(10x + 16\) — **Not equivalent**.
5. \(2(7x + 5)\) — Simplifying this: \(2(7x + 5) = 14x + 10\), which is **Equivalent**.

The correct equivalent expressions are **\(14x + 10\)** and **\(2(7x + 5)\)**.

Would you like any further details or explanations?

Here are 5 related questions:
1. What are like terms in algebra, and why do we combine them?
2. How would you simplify an expression involving multiplication and addition like \(2(7x + 5)\)?
3. Can two different-looking expressions still be equivalent? How do you determine equivalency?
4. What happens when you forget to combine like terms?
5. Why is it important to simplify algebraic expressions?

**Tip:** When simplifying expressions, always group like terms together to make calculations easier.

Select all the expressions equivalent to 12x - 3 + 2x + 13.

Learn how to simplify the expression 12x - 3 + 2x + 13. Combine like terms and apply the distributive property to find the equivalent expressions. This problem helps develop algebraic skills for students in Grades 6-8.

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