Solve each inequality. Give the solution set using interval no...

Question

Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. -2x - 2 ≤ 1 + x

Accepted Answer

Welcome back. Everyone in this problem, we want to find a solution for the inequality negative five X minus 11 is less than or equal to one plus X. And we want to provide the solution set in interval notation for our answer choices, A is open bracket negative two infinity. Close parenthesis, B is open parenthesis negative two infinity. Close parenthesis, C is open parenthesis, negative infinity, negative to closed parentheses and D is open parenthesis negative infinity, negative to closed bracket. Now, what are we trying to find here? We want the solution. In other words, we want to know what X equals. We're working with an inequality and we can use the same logic that we use as for an equation. The only difference is that no, our answer would be a solution set instead of one or two answers. So let's go ahead and see if we can solve and then figure out what our solution set would be. No. If I rewrite my equation here, then I would need to first get all my X terms on one side just like if I do it for an equation. So to do that I can subtract X from, from both sides. OK. So that I can get the excess on the left hand side of the inequality. And I can also add 11 to both sides. No, when I do that or I should write that in black. So we can distinguish what we're doing here. OK? No negative five, X minus X. That's negative six X, negative 11 plus 11 equals +01 plus equals 12 and X minus X equals zero. So negative six, X is less than our equal to 12. Therefore to get X by itself, I could divide both sides by negative six. But now remember in an inequality when we divide or multiply by a negative one, we flip the inequality side. So negative six cancels negative six that leaves me with one that has one X but no, I would write X is greater than or equal to. Because remember as I said, we divided by negative one and 12, divided by negative six is negative two. So now what's our solution set? Since X is greater than our equal to two? Well, if you think about it on a number line starting at negative two could be all the possible values of X and it also includes negative two because it's greater than or equal to negative two. So I shared my circle there. It it it includes it right? And if it includes all of the values above negative two, that means it would be going on to infinity. Therefore, my solution set is a close open bracket, negative two because negative two is included and open parenthesis infinity because infinity just continues going on and on and on. So our answer is answer a thanks a lot for watching everyone. I hope this video helped.

Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. -2x - 2 ≤ 1 + x

Key Concepts

Solving Linear Inequalities

Properties of Inequalities

Interval Notation

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