Two Ways to Solve an Absolute Inequality with Two Absolute Values | Glass of Numbers

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This may not be an SAT/ACT absolute inequality question, but it's more difficult than those seen on SAT or ACT. So, if you understand the two techniques demonstrated in this video about solving inequalities, you will become a lot better on your SAT or ACT preparation!
We are solving the inequality |x-4| greater than |x+2| in two ways:
1) Graphing
2) Testing Points
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Опубликовано:

7 сен 2024

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Комментарии : 20

@arambp77 Месяц назад

love from the netherlands

@GlassofNumbers Месяц назад

Thank you! Please help others by sharing the video with others 😁

@KTKMaths Год назад

Simple & Clear cut Explanation. Thank you so much. May I know which writing platform you are using? Seems cool in your neat handwriting..

@GlassofNumbers Год назад

Thank you! I use a samsung tablet to record the videos!

@KTKMaths Год назад

Great work. Keep up.@@GlassofNumbers

@jisotico1172 2 года назад

in method 2, why didnt you test the 4 cases (+ +, + -, - +, - -) , and only 2?

@GlassofNumbers 2 года назад

Because the third and fourth are equivalent to the first and second, i.e. (iii) -(x-4)=x+2 is equivalent to (x-4)=-(x+2) and (iv) -(x-4)=-(x+2) is equivalent to x-4=x+2.

@Bfg.. 11 месяцев назад

does this also work when an absolute value of like |x-3| is being divided by |x+3| and i like less than 2. So like would it work for |x-3|/|x+3| < 2. It might if the numbers are correct. So like move the bottom to the other side. And then do the same thing? IDK if that will work cus of the sign flipping jazz.

@GlassofNumbers 11 месяцев назад

We can first rewrite it so that it becomes |x-3|< 2|x+3|, then move everything to the left side. And it becomes a similar problem to this video's problem.

@Bfg.. 11 месяцев назад

@@GlassofNumbers ok cool thanks

@AddisShimelis 6 месяцев назад

How can we get the intersection point

@GlassofNumbers 6 месяцев назад

We can do that by setting |x-4|=|x+2|

@Taskit311 2 года назад

testing points method doesnt always work?

@GlassofNumbers 2 года назад

It works, sometimes it's just more complicated than the graphing method!

@hotcornstudios8510 2 года назад

Squaring both sides can be faster in some cases

@GlassofNumbers 2 года назад

Yes, though it doesn't always work so well!

@hotcornstudios8510 2 года назад

@@GlassofNumbers Unfortunately, true

@tomsxe Год назад

It almost never works. Because 2^2 < 3^2 but (1/2)^2 is not minor to (1/3)^2, so you have to restringe it for values around 1, and it's more complicated to do