What makes an inequality always true

View All Related Lessons. Tommy San Miguel. Inequalities with no solution or all real numbers Sometimes, it's possible to solve an inequality and realize it is meaningless! Alex Federspiel. This video by Monica Wieneke shows you some inequalities with no solution or infinite solutions. Summary You can get inequalities that are false for any variable. Try it! You've reached the end. How can we improve? Send Feedback. Pre-Algebra More about equation and inequalities Overview Fundamentals in solving Equations in one or more steps Calculating the circumference of a circle.

Pre-Algebra Graphing and functions Overview Linear equations in the coordinate plane The slope of a linear function Graphing linear inequalities Solve systems of equations by graphing. Pre-Algebra Introducing geometry Overview Geometry — fundamental statements Circle graphs Angles and parallel lines Triangles Quadrilaterals, polygons and transformations.

Special thanks to reggaemuffin for being a supporter! Vote him as a witness to help make Steemit a better place! This post has received a 1. All posts. Newcomers' Community. Steemit Feedback. Explore communities…. Inequality: Always, sometimes or never? For part b we proceed similarly. Now for the clincher! In conclusion When solving inequalities or equations, we should consider the possibility that the it may always be true, or never be true, or sometimes true.

I hope you have learned something solving these challenging inequalities. Image Credits The first picture was derived from Pixabay , while the rest are all my own work. There are actually two statements here. For a visualization of this inequality, refer to the number line below. The numbers 4 and 9 are not included, so we place open circles on these points.

Again, because the numbers -2 and 0 are not included, we place open circles on those points. However, the meaning of this is difficult to visualize—what does it mean to say that an expression , rather than a number, lies between two points?

Finally, it is customary though not necessary to write the inequality so that the inequality arrows point to the left i. However, this is wrong. What numbers work? How about ? By playing with numbers in this way, you should be able to convince yourself that the numbers that work must be somewhere between and This is one way to approach finding the answer.

The other way is to think of absolute value as representing distance from 0. Once again, we conclude that the answer must be between and This answer can be visualized on the number line as shown below, in which all numbers whose absolute value is less than 10 are highlighted. It is not necessary to use both of these methods; use whichever method is easier for you to understand.

It is necessary to first isolate the inequality:. Now think about the number line. Therefore, it must be either greater than 8 or less than Expressing this with inequalities, we have:. We now have 2 separate inequalities.