Solve each inequality. Give the solution set in interval notation...

Question

Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 2-4x+5(x-1)<-6(x-2)

Accepted Answer

Hey, everyone. Welcome back in this problem. We are asked to find the solution set for the following inequality and were told to express the answer in interval notation. And the inequality were given is one minus three, X plus nine times X minus three is less than negative, one times X minus nine. So rewriting what we're given now when we have an inequality like this, and we're asked to find the solution set. What we want to do is find all of the X values that satisfy the inequality. In order to do that, we need to isolate X. Okay. So it's just like when we solve for X and an equality, we want to get all of the X terms to one side, all of the constant terms to the other side. So let's start by expanding on both sides, we got one minus three, X plus nine, X minus 27. Okay. Make sure you're distributing that nine to both terms, both the X and the negative three is less than the same thing on this side. Make sure we're expanding and distributing that negative one to both terms. We get negative X plus nine all right. Let's move all the X terms to the left hand side and all the constant terms to the right. On the left hand side, we're gonna have negative three X plus nine X. We have negative X on the right hand side, we need to add X to move it to the right hand side. So we get plus X on the left hand side. Okay. Sorry if I said we're moving into the right, we're moving it from the right hand side to the left hand side. And then on the right hand side, we have our plus nine, We're going to subtract one to move this one over to the right hand side and then we're gonna add 27 to move that over. And so we end up with negative three X plus nine, X plus X is less than nine minus one plus 27. Alright. So let's simplify negative three X plus nine X plus X is going to give us seven X nine minus one plus 27 is gonna give us 35. And so we get seven X is less than 35 dividing both sides by seven. We get that seven or sorry that X is less than five. And so this is the solution set. Okay, this is all the X values that satisfy the inequality. As long as X is less than five, the inequality is satisfied. And so to write this in interval notation and we want X less than five. So five is going to be the upper limit of our inequality or of our interval. Sorry, we have a round bracket to indicate that we don't include five because we want X less than five, but X can't be exactly five. Okay. So round bracket to indicate that five is not included and then we have any value all the way from negative infinity. Okay. So any value from negative infinity up to five, but not including five is included in our interval and that is going to correspond with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

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Solve each inequality. Give the solution set in interval notation. See Examples 1 and 2. 2-4x+5(x-1)<-6(x-2)

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