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In $15-26,$ find and graph the solution set of each inequality.$$2|x+2| > -3$$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 1

The Real Numbers and Absolute Value

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $15-26,$ find and graph…

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Solve each inequality. Gra…

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Solve each inequality, and…

Okay, so we want to solve this problem two times absolute value of X plus two is greater than Agnes three. So, in order to solve this problem, the first thing I'm gonna dio is the viable sides by two. In order to get my absolute value exposed to by itself until we get X Plus two is bigger than negative three to read it by two. Because the negative 1.5 here's kind of the kicker about this problem. If you think about it in terms of a number line and in terms of absolute value, number is bigger than a negative. 1.5 include numbers like negative one negative, 1/2 zero, one to and three. And it keeps going on infinitely. However, this interval right here is an interval that we can't actually achieve. We can't show numbers like negative one or native. 1/2 night of one can't be result of an absolute value because all absolute values yield positive numbers is their answer. And so, since this is the absolute value of exports to write, not just expose to because it was absolute value exposed to before, I actually can't get anything in this range for my solutions and so and ordered us continue to solve this problem I have toe on. Lee use numbers in the solution set that actually are bigger than negative 1.5. So my solution shut. Technically, should be anything with values in here. Absolute values that get me a throwing bigger than negative 1.5. But when we look at that, in reality, we can't get a negative number. So we're actually just focusing on anything bigger than zero him. So either what's inside this absolute value X plus two is bigger than zero or it's smaller than zero. And why did I put that foreign? Because that's kind of confusing. When you look at an absolute value, it could be a number that's positive or negative on the inside of your absolute value. So, for example, negative, too absolute value of that. Be positive, too, which is still a distance greater than zero right. Positive to the absolute value of that would also be positive, too, and that also would have a distance of zero. So either whatever's inside here is bigger than zero, or it's a negative number, which, when you take the absolute value of it is still going to be bigger than zero. So either it's a negative number that we get out of this or it's a positive number. So I subtract full size by two. We have X is bigger than negative to or X is smaller than, um, subtracted from bull signs. Negative, too. So if the number is bigger than negative two or smaller than negative too, then the solutions are all numbers bigger than negative. Teoh were smaller. The negative shoes on a graph We're just gonna draw number line here is negative. Two. It's not equal out negative. Two. We know that because there's no less than or equal, then sign. It's just a plain symbol last, then looks like this alright, less that looks like that greater than looks like that less than are equal to greater than or equal to. Those are the ones that have solid lines. Since there was no line underneath, we know we're leaving an open circle, so if we have X is greater than negative. Two things greater than negative Teoh are to the right or X is smaller than negative, too. Those things air to left, so really our answers all rial numbers except negative too

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