In Exercises 85–96, simplify each algebraic expression. 7−4[3−...

Question

In Exercises 85–96, simplify each algebraic expression. 7−4[3−(4y−5)]

Accepted Answer

Welcome back. I'm so glad you're here. We've got an expression and we're to simplify it. Let me rewrite that a little bigger three minus three times bracket, three minus parentheses, three minus Y. And parentheses and brackets. So what are we doing? Well to simplify, we recall from previous lessons the acronym penned as which reminds us of the order of operations. We start with parentheses, then go through exponents and then multiplication and division from left, right and addition and subtraction from left to right. And with this particular one we want to note with addition and subtraction that we are only going to add and subtract like terms because we've got a bunch of threes and why and the reason why are not like terms. So let's start with parentheses with P. And we always start with inner most parentheses. And I just want to note again a quick note that parentheses and brackets both function as parentheses. They just use Brackets alternating. So you don't get lost in parentheses and you can keep track a little bit easier which one you're working on? And we're always going to start working with the one that is innermost. So the innermost parentheses here is three -Y. And what operation is going on there? It's subtraction. Can we subtract three minus y. We can't they're not like terms so we can't do that. And we ask ourselves is this parentheses functioning for multiplication in any way meaning is there a number squished up against this parentheses that's going to be distributed to the numbers inside. And yes, in this case there's a negative one that needs to be distributed to both of these terms? Both to the three and to the negative Y. So there's multiplication happening on inside these bigger parentheses. And then there's also subtraction here. In which one do we do first? In the order of operations? We're going to do the multiplication. So let's distribute that negative one negative one times three is negative three negative one times negative Y. Is positive Y. And that has gotten rid of those innermost parentheses and we can bring everything else down. We've got three minus three bracket, three minus three plus Y. End bracket. So we've still got these parentheses that are the brackets to deal with and what's going on inside of there? Well we've got subtraction and addition and we can only add or subtract like terms. So which one has like terms will the three minus three. So we can take three minus three. Well three minus three equals zero. So I'm not even going to bother writing that when we bring it down. We've just now got three minus three bracket and all that's left in there is the why and the bracket. So we're still trying to reduce our parentheses here and all that is left here is just the parentheses around the Y. There are no operations happening inside. So is it functioning for multiplication. Yes this negative three needs to be multiplied by the Y. So we've got multiplication happening here. This is subtraction. Which one do we do first? Again? We're doing multiplication. So negative three times. Why is negative three? Why? Because we can multiply and divide terms that are not like terms. We'll bring down the rest. Which is this three? So we've got three minus three Y. The only operation happening here is subtraction. We've got a three and a minus three Y. Well those are not like terms and we can't subtract like terms. So that's as simplified as it's going to get three minus three Y. Which matches answer choice C. Well done, we'll catch you on the next one.

In Exercises 85–96, simplify each algebraic expression. 7−4[3−(4y−5)]

Key Concepts

Order of Operations

Distributive Property

Combining Like Terms

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