In Exercises 117–130, simplify each algebraic expression. 7-4[3-(...

Question

In Exercises 117–130, simplify each algebraic expression. 7-4[3-(4y-5)]

Accepted Answer

Welcome back. I am so glad you're here. We are asked to simplify the expression minus three, multiplied by open bracket. Seven minus open parentheses. Five X minus nine, closed parentheses, close bracket. And our answer choices are answer choice, A 15, X minus 34 answer choice, B negative 15, X plus 21 answer choice C 15, X plus seven and answer choice D negative 15, X minus 26. All right, we recall from previous lessons that when we have an expression, we need to follow the order of operations that will start with parentheses, followed by exponents and then we'll have multiplication and division from left to right and then addition and subtraction from left to right, otherwise known as the acronym. So here we look for parentheses. We want to start with the innermost parentheses and the innermost parentheses. Here are this five X minus nine and recalling that both parentheses and brackets function as parentheses in this expression. So we want to simplify five X minus nine. However, we can only add and subtract like terms. We cannot take five X minus nine. So how do we get rid of those parentheses? Well, we look in front of the parentheses and see if, if there's anything in front of the parentheses that needs to be distributed to what's inside the parentheses. And in this case, we have this negative and really what it is is it's a negative one, the negative one needs to be distributed to both terms inside of the parentheses. So let's do that. We'll take negative one multiplied by five X which is negative five X and negative one multiplied by negative nine, which is a positive nine. So we put plus nine and now we've gotten rid of those innermost parentheses and we can bring down everything else. That's part of our expression. So in front of this negative five X, there's a seven and then this is all inside of brackets still. And then in front of the brackets, we have 14 -3. So now we are dealing with our second set of parentheses, which is the brackets and we want to do the operations taking place inside of there and we can only add and subtract leg terms here. The leg terms are seven plus nine and seven plus nine is 16. Now, we can bring down everything else from the expression. The 16 is having five X subtracted from it. So we have 16 minus five X that's still in brackets and in front of the brackets is 14 -3. Now to get rid of the brackets, we want to distribute what's in front of them, which is this negative three. So we can take negative three multiplied by 16, which is negative 48 negative three multiplied by negative five X which is a positive 15 X. And now bringing down what's left is just this 14 in front. Now we want to combine like terms, we have the parentheses gone, no exponents, multiplication and division is done. It's just adding and subtracting like terms and the like terms here are minus 48 14 minus 48 is negative 34. And then bring down what's left is plus X. Now to match with our answer choices, we can switch the order of these terms. We can put the 15 X first Then -34. And we look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

In Exercises 117–130, simplify each algebraic expression. 7-4[3-(4y-5)]

Key Concepts

Order of Operations

Distributive Property

Combining Like Terms

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