If we map both those possibilities on a number line, it looks like this: This notation tells us that the value of g could be anything except what is between those numbers. A quick way to identify whether the absolute value inequality will be graphed as a segment between two points or as two rays going in opposite directions is to look at the direction of the inequality sign in relation to the variable. Identifying the graphs of absolute value inequalities If the absolute value of the variable is less than the constant term, then the resulting graph will be a segment between two points.

You could have simplified this in other ways, but I usually find it easier to get rid of the negative right away. However, the inequalities that occur between the two sides may be combined with an "or".

The same principle holds with the two parts of the absolute value. I told you it all fits together. I know you're going to be tired of hearing me say it, but it is much easier to understand if you see the big picture.

Greater Than When the absolute value is greater than the right hand side, then the answer will be in two parts, with an or separating them.

It will be greater than the right hand side or less than the opposite of the right hand side. Absolute Values the Geometric Way I have no problem with using the geometric approach to solving absolute value inequalities.

Not the geometric approach where you put it into the calculator, but the geometric approach where you use the geometric definition of absolute value. The geometric definition of absolute value is the distance from 0 on the number line.

However, this technique requires that you know some of the properties of absolute values. These are good things to know anyway isn't it all? Let's consider the same inequality that we solved before: This says that the distance from 3 on the number line is less than or equal to So, start at 3 and go 20 to the left and 20 to the right You need the distance to be less than or equal to 20 units away.

This would include values between and Since the equal to is included, you include the endpoints to get the answer interval notation of [,23].

That was easy, you say. A little bit harder problem: Here's where those properties of absolute values come into play. The absolute value of the opposite of a number is the same as the absolute value of the number.

Polynomial Inequalities Polynomials are continuous. That means that you can draw them without picking up your pencil there's a more rigorous definition in calculus, but that definition will work for us, now.

If you're going to change from being less than zero to being greater than zero and you can't pick up your pencil, then at some point, you must cross the x-axis. That means that the only place the inequality can change is at an x-intercept, a zero, a root, a solution.

The key then, to finding the solution set for a polynomial inequality, is to find the zeros of the inequality pretend it was an equationputting them on the number line, and picking a test point in each region.

Write the polynomial inequality in standard form so that the right side is zero.A beautiful, free online graphing calculator from timberdesignmag.com timberdesignmag.com6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending.

plot or draw linear and quadratic inequalities and systems of inequalities with our free step-by-step math solver and grapher Enter the polynomial inequalities you want to plot, in terms of the variables x and y, set the limits and click the Plot button.

Example 2 Write an algebraic expression for: A certain number decreased by four.

To square a number you multiply it by itself. For example 3² =3×3=9. To cube a number you multiply it by itself three times. So 3³=3x3x3= If you are studying GCSE it is very helpful to learn the common squares and cubes to save you time in the non calculator exam.

Math homework help. Hotmath explains math textbook homework problems with step-by-step math answers for algebra, geometry, and calculus.

Online tutoring available for math help. This calculator will solve the linear, quadratic, polynomial, rational and absolute value inequalities.

It can handle compound inequalities and systems of inequalities as well. To graph inequalities, use graphing calculator.

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