Equation and Inequation With Absolute Value [12th Grade]

[shawqidu19]

Homework Statement

Resolve these equations and these inequations with the absolute values. Give the solutions in the form of interval :

|2-x|< 4

|6-2x| = 3

|x+2| > 3

|4x²-12x+9| = 4

|3x+1|+|1-x|>3

|1-x²|=2x

|x+2|<|x+3|

|x^3-1|+pi&amp;gt;\sqrt{3}&lt;br /&gt; &lt;br /&gt; 3&amp;lt;|x+2|&amp;lt;4&lt;br /&gt; &lt;br /&gt; &lt;br /&gt; &lt;br /&gt; &lt;br /&gt; &lt;h2&gt;Homework Equations&lt;/h2&gt;&lt;br /&gt; &lt;br /&gt; &lt;br /&gt; &lt;br /&gt; &lt;h2&gt;The Attempt at a Solution&lt;/h2&gt;

 

[arildno]

Way too hard to solve without some hints.
Have you done some work to help me out with?

 

[jacobrhcp]

you should try do them yourselves, I'm sure that if you think about them you can solve them =).

to get a 'feel'

|y|<c if and only if

-y>-c ánd y<c

if there is one you get stuck on, I or someone else will help you as you've shown what you've tried.

 

[HallsofIvy]

I have always felt that the best way to handle complicated inequalities is to first solve the connected equation (|2- x|= 4, etc.) The points where the two sides are equal separate "<" and ">".