In Exercises 117–130, simplify each algebraic expression.

8(3x-...

Question

In Exercises 117–130, simplify each algebraic expression.

8(3x-5)-6x

Accepted Answer

Welcome back. I am so glad you're here. We are asked to simplify the expression. We're given 12, multiplied by open parentheses. Four X minus 10 closed parentheses minus seven X. And our answer choices are answer choice. A 48 X plus 127. Answer choice B 41 X plus answer choice C 48 X minus and answer choice D 41 X minus 120. All right, we look at our expression and in order to simplify it, we recall from previous lessons, the order of operations will start off with parentheses, followed by exponents, followed by multiplication and division from left to right and then addition and subtraction from left to right or the acronym peda. So starting with parentheses, we have one set of parentheses here. It's this four X minus 10. So we want to do the operation inside of the parentheses, which is subtraction. However, with subtraction, you can only subtract like terms and four X and 10 are not like terms. So we look in front of the parentheses and see if there's a number squished up in front of them. That needs to be distributed to the terms inside of the parentheses. In this case, it's a 12, we have a 12 that needs to be multiplied by both four X and negative 10. So we take 12 multiplied by four X. That's going to be 48 X and then we take multiplied by a negative 10. That's going to be a negative 120 or we put minus 120. And then we bring down anything that wasn't part of this operation, which is this minus seven X. And now there are no more parentheses, there are no exponents, there's no more multiplication that needs to take place and there's no division. So now it's just adding and subtracting like terms. The only like terms here are 48 X and this negative seven X. So we take 48 X minus seven X and that leaves us with X and then we can bring down what's left, which is this negative 120. So we have 41 X minus 120. And this is as simplified as this one is going to get, we look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

In Exercises 117–130, simplify each algebraic expression. 8(3x-5)-6x

Key Concepts

Distributive Property

Combining Like Terms

Simplifying Expressions

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