Solve each inequality. Graph the solution set and write the set in interval notation. 5<(1)/(2)

Solve each inequality. Graph the solution set and write the...

Key Concepts

Compound Inequalities

Compound inequalities involve two distinct inequality relations that are combined into a single statement, and the solution must satisfy both inequalities simultaneously. Understanding how to break down and solve each part of a compound inequality is essential to accurately finding the values that meet all the conditions.

Solving Linear Inequalities

Solving linear inequalities involves isolating the variable on one side of the inequality sign by performing permitted algebraic operations, such as addition, subtraction, multiplication, or division. It is important to remember that multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.

Graphing on a Number Line

Graphing a solution set on a number line provides a visual representation of all numbers that satisfy the inequality. This includes placing open or closed circles at the endpoints depending on whether the endpoint values are excluded or included in the solution set, and shading the region corresponding to the solution.

Interval Notation

Interval notation is a concise way to describe a set of numbers by specifying its endpoints and whether these endpoints are included. Parentheses indicate that an endpoint is not included in the interval, while square brackets denote that the endpoint is part of the interval.

Transcript

00:01 Here there, so for this problem, we are working with inequalities and how to solve them.

00:07 Also how to graph the solutions onto a number line and rewrite the solutions into set builder notation and interval notation.

00:17 So we're actually going to step above in the sense that we're solving all compound inequalities.

00:24 And the compound inequality we're going to work with is that five is less than.

00:31 One half x which is less than six.

00:41 All right.

00:42 So to get started with this problem, again, you always want to isolate your variable, and the variable is kind of in the middle of this inequality.

00:49 And so in order to isolate it, it's being multiplied to one half.

00:54 There's two different ways you can go through to get rid of that.

00:58 So you could simply divide by a half and go through the process of dividing a whole number with a fraction by making it.

01:06 A fraction and then doing the keep change flip method or i'm just going to simplify this by okay how else do it can i get rid of this fraction you may know that you can get rid of this fraction by multiplying by its reciprocal and so the reciprocal would be that fraction flipped and so what i mean by that is i'm going to multiply every piece of this inequality by two over one again if you have not gone through with the approach of multiplying by the reciprocal it actually is similar to dividing by one half on both sides and then going through the keep change flip because when you do the keep change flip you are actually multiplying by the fraction two over one and so that is the same as multiplying by the reciprocal which is two over one but please do use whatever method you are more comfortable with i'm going to go with this method by multiplying with reciprocal.

02:17 All right...

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