Algebra - Absolute Value Inequalities

Absolute value is always positive, so why not take a lesson from it and always be positive too? Absolute value inequalities are somewhat challenging, no matter how positive you're feeling. We investigate bifurcation and other scenarios. Good energy for this lesson, YAY MATH!
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The square bracket means "include" that number. The rounded parenthesis mean "don't include" that number. I hope this helps!

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@@malindakaymiller Malinda, thank you so much for your kind words.

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Great explanation of "or" and "and" with non-math related examples.

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I like how you teach math. My younger and I actually understand what math you go through. Right now, we are on absolute value ptoblems. It makes sense now. I do have a question about the ones where all real numbers are the answer. So, you don't have to plot the two points that you get when you solve the two equations?

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at 26:21 was confusing me because i thought you didn't change the sign, but it should read -3 + -10 = -13

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[@Konnoisseur]

Hmmm I'm not so sure about the problem starting at around the 22 minute mark. |5x| < -7 does have solutions. It's either 5x < -7 and 5x > 7 which simplifies to x < -7/5 or x > 7/5

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[@mohamedjameel2283]

Dear Sir, How to find the Absolute Value Inequalities of this ? please provide me the step of answer -5 < 3 - 2x ≤ 7

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[@HighFiveGuy13]

So how would you solve something like -2 > 3(x+1) + 1 ≤ 2 ?

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[@ujjwalrawat5105]

Sir, my doubt is, your trick doesn't somehow apply to this problem ((x^2-7|x|+10/(x^2-6x+9))

[@isabellaw1070]

Can you explain the brackets and parenthesis way to right these?

[@inhabitantofearth]

THANK YOU for this! Absolute values confused me so much!

[@owsomebrain]

The last inequality, when he subtracted 10 from both sides, the sign should have flipped right? since it was

[@inhabitantofearth]

No. You only flip the sign when you multiply or divide both sides by a negative number.

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Danielle Byrd Cool. Thanks

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[@HighFiveGuy13]

Can you put some key notes sometimes on hard topics in you descriptions please?

[@yaymath]

HighFiveGuy13 Hi HighFiveGuy! All notes available on yaymath.org, under Videos. Thank you for asking!

[@evelyny8579]

why is the expression inside absolute values signs taken out

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17:30, "Mr. Smith is a Genius"

[@thegreenman941]

How would you solve │x^2+4│≥ 5x ?

[@jamesconnelly4354]

is that interval notation??

[@aravwijesinghe5276]

why did he not change the sign to positive 7 on the last problem? He kept it as 5x > -7. I thought whenever you change the inequality sign you have to change the number sign.

[@boolinbooler9319]

You can also write the "And" problemes like -12 > x > 12

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It all makes sense now

[@dianayo1975]

That means your lines are extending from 8 to infinity (positive infin), and your other line is extending from - infinity to -5.

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Open means that on of them is greater or less than and not equal to. Close means that they are greater or less than or equal.

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yaymath..can u help me in my homework??/ find the solution set of |X^2 - 17|greater than or equal to 8 find solution set of |3X - 2| = |2x + 3|......thnx

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im confused on what way the lines are shaded on the number line :/

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that two parallel lines | | is called mod??

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13:09 14:18 17:13 28:40

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