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Question Video: Addition and Subtraction of Algebraic Expressions Mathematics • 7th Grade

Charlotte has 2𝑥 + 7 dollars. She gives 3𝑦 − 2 dollars to Benjamin and then receives 𝑥 − 𝑦 dollars from Jacob. Write a simplified expression for the remaining amount of money, in dollars, that Charlotte has.

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Video Transcript

Charlotte has two 𝑥 plus seven dollars. She gives three 𝑦 minus two dollars to Benjamin and then receives 𝑥 minus 𝑦 dollars from Jacob. Write a simplified expression for the remaining amount of money, in dollars, that Charlotte has.

We first note that the amount of dollars that Charlotte has will be the amount she starts with minus the amount she gives away plus the amount she receives. She starts with two 𝑥 plus seven dollars. She gives away three 𝑦 minus two dollars, so we need to subtract this. She then receives 𝑥 minus 𝑦 dollars, so we need to add this. Our expression is two 𝑥 plus seven minus three 𝑦 minus two plus 𝑥 minus 𝑦.

Next, we need to collect the like terms. Two 𝑥 plus 𝑥 is equal to three 𝑥. Negative three 𝑦 plus negative 𝑦 is the same as negative three 𝑦 minus 𝑦, which equals negative four 𝑦. Finally, seven minus negative two is the same as seven plus two, which equals nine.

Our expression therefore simplifies to three 𝑥 minus four 𝑦 plus nine. This is the total number of dollars that Charlotte now has.

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