Equation and Inequation With Absolute Value [12th Grade]

In summary, the conversation is discussing how to solve equations and inequalities involving absolute values, with the solutions being given in the form of intervals. The person providing the summary suggests solving the connected equation first and using the points where the two sides are equal to determine the intervals for the solutions. They also mention asking for help if needed after showing what attempts have been made.
  • #1
shawqidu19
10
0

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|+[tex]pi[tex]>[tex]\sqrt{3}[/tex]

3<|x+2|<4




Homework Equations





The Attempt at a Solution

 
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  • #2
Way too hard to solve without some hints.
Have you done some work to help me out with?
 
  • #3
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.
 
  • #4
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 ">".
 

What is an absolute value equation?

An absolute value equation is an equation that contains an absolute value expression (such as |x|) and requires finding the values of the variable that make the expression inside the absolute value equal to a given number. These equations often have two solutions.

How do you solve an absolute value equation?

To solve an absolute value equation, isolate the absolute value expression and rewrite it as two separate equations without the absolute value. Then solve each equation separately for the variable and check the solutions in the original equation.

What is an absolute value inequality?

An absolute value inequality is an inequality that contains an absolute value expression (such as |x|) and requires finding the values of the variable that make the expression inside the absolute value greater than or less than a given number. These inequalities often have multiple solutions.

How do you solve an absolute value inequality?

To solve an absolute value inequality, isolate the absolute value expression and rewrite it as two separate inequalities without the absolute value. Then solve each inequality separately for the variable and combine the solutions to find the final solution set.

What are some real-life applications of absolute value equations and inequalities?

Absolute value equations and inequalities can be used to solve problems involving distance, temperature, and time. For example, the distance between two points on a coordinate plane can be represented by an absolute value equation, and the temperature range for a specific location can be represented by an absolute value inequality.

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