In Exercises 121–128, write each English phrase as an algebraic e...

Question

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Eight decreased by three times the sum of a number and six

Accepted Answer

Hello. Today we're going to be rewriting an algebraic sentence as an algebraic expression. So the sentence given to us is four times the sum of the number X and two decreased from 12. So let's just go ahead and take a look at the first half of the sentence four times the sum of the number X and two. What this part means four times is that we're taking the number four and we're multiplying some quantity by it. And the second part of this is the sum of the number X and two. So we're taking four times the sum of the number X and two. But the sum of X and two is X plus two. So what's going on in this first half is we're taking four and we're multiplying the quantity X plus two by four. And now paying attention to the second half of the sentence. This entire quantity is being decreased from 12. So that means that we're taking this entire quantity and we're subtracting it from a number 12. So the entire sentence expressed as an algebraic expression is minus four times X plus two. Now, what we want to do is go ahead and simplify this. In order to start simplifying this, we're going to distribute negative 42 X. And to doing so is going to leave us with minus negative four times X which is negative four X times I'm sorry minus, negative four times two which is negative eight. Now we need to go ahead and combine like terms the only like terms that are combined herbal are positive 12 and negative eight and what that leaves us with is four minus for X. Now, if you notice we have factors of four in both of these numbers so we can go ahead and factor out a four from this expression. Doing so is going to give us four times one minus x. This is gonna be the simplest form of this algebraic sentence and therefore this is the simplest algebraic expression to this sentence. And that means that the answer to this problem is going to be a So I hope this video helps you in understanding how to write an algebraic expression from a sentence and I'll go ahead and see you all in the next video.

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