Express your answer using set notation or interval notation. Graph the solution set. |2 x-3| ≥2

Name: Problem 45, Chapter 1: Algebra and Trigonometry
Uploaded: 2020-07-09T19:52:28-08:00
Duration: 4 min 10 s
Channel: Joshua Fischbach
Description: Express your answer using set notation or interval notation. Graph the solution set. |2 x-3| ≥2

step 1 All right, so we're solving the absolute inequality. 2x minus 3 is greater than equal to 2. You'

Express your answer using set notation or interval notation....

Key Concepts

Interval Notation

Interval notation is a concise method for describing subsets of the real number line. It uses brackets and parentheses to indicate whether endpoints are included (closed intervals) or excluded (open intervals), and is commonly used to express solution sets of inequalities.

Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of its direction. It is used to measure magnitude without considering positive or negative signs.

Absolute Value Inequalities

Inequalities involving absolute values, such as |ax + b| ? c, require splitting the inequality into two separate cases because the expression inside the absolute value can be either nonnegative or nonpositive. This typically results in a compound inequality where ax + b is either greater than or equal to c or less than or equal to -c.

Transcript

00:01 All right, so we're solving the absolute inequality.

00:02 2x minus 3 is greater than equal to 2.

00:05 You're going to remove the absolute value sign, and you're going to take the inside value, and you're going to set two possibilities up.

00:13 One possibility is that exactly what you see is what you get, so 2x minus 3 is greater than are equal to 2.

00:19 The other possibility is that the opposite is true, that 2x minus 3 is not greater than or equal to, but less than are equal to, not positive 2, but negative 2.

00:29 And when you set the other possibility of the opposite possibility, it's really like you take this one on the left and you multiply by a negative one.

00:36 That would be the same idea, right? so it's either that value or relationship or the opposite of that relationship.

00:43 And now we solve both of these scenarios.

00:46 So the way you're going to do that is you want to get the x by itself.

00:49 So you're going to add three to both sides.

00:52 And the result is that on the left relationship, you get 2x is greater than equal to 5.

00:59 And on the right relationship you get 2x is less than or equal to 1.

01:05 And then you're going to divide both sides by two and both processes solve for either one of these inequalities.

01:11 Because you want to not having the value of 2x, you want the value of 1x.

01:15 And you get x is greater than or equal to 5 halves, which is 2 .5.

01:21 And on the other side over here, you get x is less than or equal to 1 half, which is just a half.

01:29 So it makes sense to use the interval of one half when we do our graph.

01:33 So we're going to go up to our graph.

01:34 We're going to count by one half.

01:35 We need to include one half and two and a half.

01:37 So i'll just start with zero.

01:39 And then we've got one, two, three.

01:46 So that means that this is two and a half and that this is one half.

01:51 Okay.

01:52 And now you're going to close dots because this includes the values that you're looking at as endpoints, right? because it's squared that equal to or less than equal.

02:01 To.

02:01 So that means we're going to have a closed dot at two and a half...

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