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Decide whether 2x + 8 and 2(x + 4) + 4 are equivalent expressions. Explain how you know.

User David Guan
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Answer: Yes, they are equivalent expressions.

Explanation:

To show that two expressions are equivalent, we need to simplify both expressions and show that they are equal.

Starting with the first expression:

2x + 8

We can see that there are no common factors we can factor out, so this expression is already simplified.

Now let's simplify the second expression:

2(x + 4) + 4

Using the distributive property, we can simplify this as:

2x + 8 + 4

Simplifying further, we get:

2x + 12

Now we can see that the two expressions are equivalent since 2x + 8 and 2x + 12 represent the same value for any value of x. Therefore, we know that the two expressions are equivalent.

User Glv
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