What makes an inequality strict

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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. Consider them independently. Now think: the absolute value of the expression is greater than —3. What could the expression be equal to?

And 0. And 7. And — Absolute values are always positive, so the absolute value of anything is greater than —3! All numbers therefore work. Privacy Policy. Skip to main content. Introduction to Equations, Inequalities, and Graphing. Search for:. Learning Objectives Explain what inequalities represent and how they are used.

Key Takeaways Key Points An inequality describes a relationship between two different values. Inequalities are particularly useful for solving problems involving minimum or maximum possible values. Key Terms number line : A visual representation of the set of real numbers as a series of points.

Learning Objectives Solve inequalities using the rules for operating on them. If both sides of an inequality are multiplied or divided by the same positive value, the resulting inequality is true. If both sides are multiplied or divided by the same negative value, the direction of the inequality changes.