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.