Question

theresa wrote the expression 4(x + 3) + 10 to represent how much she and her friends spent on lunch in all. maria wrote the expression 4·x + 4·3 + 10 to represent the same situation. are these expressions equivalent? explain your reasoning.

Explanation:

Step1: Apply distributive property

For the expression $4(x + 3)+10$, by the distributive property $a(b + c)=ab+ac$, we have $4(x + 3)=4\cdot x+4\cdot3$. So $4(x + 3)+10=4\cdot x+4\cdot3 + 10$.

Step2: Compare expressions

The first - expression $4(x + 3)+10$ simplifies to the second - expression $4\cdot x+4\cdot3 + 10$.

Answer:

Yes, the two expressions are equivalent because when we apply the distributive property to $4(x + 3)+10$, we get $4\cdot x+4\cdot3 + 10$.