Solving Absolute Value Equations and Inequalities - Number Line & Interval Notation - Algebra

This algebra video tutorial shows you how to solve absolute value equations with inequalities and how to plot the solution on a number line and write the answer in interval notation. This video also shows you how to identify cases of no solution or infinitely many solutions / all solutions. This video contains plenty of examples and practice problems including absolute value problems with fractions and variables.
Plotting Inequalities on a Number Line:
• How To Plot Inequaliti...
How To Solve Linear Inequalities:
• How To Solve Linear In...
Solving Absolute Value Inequalities:
• Absolute Value Inequal...
Graphing Linear Inequalities In 2 Variables:
• How To Graph Linear In...
Graphing Systems of Linear Inequalities:
• Graphing Systems of Li...
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How To Solve Compound Inequalities:
• How To Solve Compound ...
Quadratic Inequalities:
• Quadratic Inequalities
Polynomial Inequalities:
• Solving Polynomial Ine...
Rational Inequalities:
• Rational Inequalities
SAT Math - Inequalities:
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Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
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Another tip: to make sure you've graphed right - if the sign is < in the original equation, you will always have one answer. If it's > you will have two or more answers, like the first two examples he provided. Great and informative video! Thoroughly explained! :)

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For the inequalities: abs.val. of 2x+1 < - 1/2 and abs.val. of 2x+1 > - 3/4 , please explain why the range of possible values for x is ( - inf , + inf ) and not ( - 3/4 , - 1/2 ).

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I have a question for Eg 2. |2/3x-1/4|>5. Do we not change the signs of the inequality when dividing? Thus making x-57/8

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6.46 guys I have a question..... Doesn't the direction only changes if - 1/2 is with the variable x?? I am confused 😢

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I like to ask a question. What are the values of n that satisfy the condition 1/|n| > n? (a) 0

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[@mathtutor-jo-anneventevoge6880]

Re the problem you start at about 6:00, I don't see why the answer isn't "all real numbers" after you find that the absolute value portion is greater than -1/2 since all abs values are positive. Thank you

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Well, negative to positive infinity or vice versa is basically equal to all real numbers, which depends on how you would like to write the domain or range of a function. If you prefer interval notation, it would be negative to positive infinity or vice versa. If in set notation, it would be all real numbers.

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12:02 Unless... theres a negative number like so -1|2x+4| "is less than or equall to" -8. I coudnt use the symble for that type of sign so i used words.

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Good day sir! I have a question clarification is it okay to put the lowest value of fraction before the highest one on the line? For instance (-1/4 before -3/4?.

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isnt -3/4 less than -1/4? so putting -1/4 before -3/4 wouldn’t matter. idk i am dumb

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One more thing What if we have an isolated absolute value one the left side, and more than 2 terms on the right side (also maybe with a variable x) lets say ( |x+2| > +9 -2x) we change the direction of the inequality sign right ? and the sign ??? does it become (+9-2x,-9+2x) ??

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at 6:30 why dont we do +2? to both sides? or in the beggining of that problem why don't we just do 4-2 = 2 and then subtract 2 to both sides?

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for the 1st question ,why did the inequality sign change to less than for the other equation?

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this is probably irrelevant now one month later, lol, but when taking the absolute value, you must take the positive and the negative of the expression. And the rule is, when multiplying or dividing by a negative, the inequality sign must change with it or the expression is false.

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Inequalities aren't like equations, when you multiply a negative number to both sides, you have to change the sign.

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In example 3 can we substract b.s by 4 other than 2

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