High School Absolute Value Inequalities: Solving for x

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To solve absolute value inequalities, one must apply the properties of absolute values correctly. The next step typically involves setting up two separate inequalities based on the definition of absolute value. If the initial setup is correct, simplifying the inequality can lead to finding the values of x. It's important to ensure that any transformations maintain the inequality's integrity. Understanding these steps is crucial for successfully solving the problem.
jenrespect
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Please help me. What is the next step to get rid of the absolute value?

uploadfromtaptalk1444438526887.jpg


I tried using its property but I don't know if its correct.

uploadfromtaptalk1444438588314.png
 
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*REDACTED*

I'm not sure my advise is right. Not thinking super straight today. XD
 
jenrespect said:
Please help me. What is the next step to get rid of the absolute value?

View attachment 89957

I tried using its property but I don't know if its correct.

View attachment 89958
Is this a homework question? Homework questions need to be posted in the Homework & Coursework sections.
 
Matterwave said:
*REDACTED*

I'm not sure my advise is right. Not thinking super straight today. XD

If the last image were correct, you could just solve it with the nominator equivalent to zero, and even if it weren't, you could still multiply through by the denominator leaving the nominator less than or equal to 0, right? Assuming what I said is correct, then it shouldn't be too difficult to find the x values.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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