# Write an inequality for a number line

Split the equation into two separate equations: the first with the absolute value term removed, and the second with the absolute value term removed and multiplied by But can an absolute value ever be negative, let alone be less than a negative?

Please accept "preferences" cookies in order to enable this widget. DO NOT try to write this as one inequality. Simplify the process by splitting the equation or inequality into two separate solutions before graphing. And, by the way, the correct conjunction is "or", not "and".

### Writing inequalities from a number line pdf

In this inequality, they're asking me to find all the x-values that are less than three units away from zero in either direction, so the solution is going to be the set of all the points that are less than three units away from zero. They're asking you for the x-values that will make the absolute-value expression greater than a negative number. Don't waste a lot of time trying to "solve" this; just write down "no solution". Therefore, we use "or" for these types of solutions. Updated April 24, By Karl Wallulis Absolute value equations and inequalities add a twist to algebraic solutions, allowing the solution to be either the positive or negative value of a number. First, I'll start with a number line. Try the entered exercise, or type in your own exercise. Click "Tap to view steps" to be taken directly to the Mathway site for a paid upgrade. He has written for the Guide to Online Schools website, covering academic and professional topics for young adults looking at higher-education opportunities. Because the variable is contained within one interval. Where the solution to an absolute-value equation is points like in the graphic above , the solution to an absolute-value inequality or "inequation" is going to be intervals. Half of six is three.

Draw solid lines visibly thicker than the number line to show the set of values that the variable can take. In this inequality, they're asking me to find all the x-values that are less than three units away from zero in either direction, so the solution is going to be the set of all the points that are less than three units away from zero.

Affiliate Even when the inequalities are more complicated, the above pattern still holds.

### Graphing inequalities

The number 2 will work, as will —2. Half of six is three. So there is no solution to this inequality; it doesn't even make sense. Draw a number line with 0 and the two points clearly labeled. So "and" is the correct conjuction. First, I'll start with a number line. The something will be the part with the variable in it. By the way, the correct conjunction for "less than" absolute-value inequalities is "and". Split the equation into two separate equations: the first with the absolute value term removed, and the second with the absolute value term removed and multiplied by The something is the piece in the middle, where the variable is. DO NOT try to write this as one inequality. Draw a number line with 0 and the two points clearly labeled make sure the points increase in value from left to right.

Then I'll solve the linear inequality. Isolate the variable in both equations to find the two solutions of the absolute value equation. Photo Credits.

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