Petrus said:Hello MHB,
solve \(\displaystyle ||x|-2|+|x+1|=3\)
and we find that \(\displaystyle x=0,-2,2,-1\)
I got problem to find the 'case',
Regards,
\(\displaystyle |\rangle\)
I don't mean those are the answer, but those are the point we should check \(\displaystyle \geq\) or \(\displaystyle \leq\), I hope you did understand.I like Serena said:That doesn't look like the right solution...
Talking about cases, what if x<-2? Or -2<x<-1? And what about -1<x<0? Or perhaps 0<x<2? And x>2?
Petrus said:I don't mean those are the answer, but those are the point we should check \(\displaystyle \geq\) or \(\displaystyle \leq\), I hope you did understand.
Can I also check this one insted of -1<x<0
-2<x<0?
Thanks, got the correct answer now :)I like Serena said:Sure you can. It's just that |x+1| does something funny at x=-1.
Absolute value is a mathematical concept that represents the distance of a number from zero on a number line. It is always a positive value and is denoted by the symbol "|" before and after the number.
To solve for x in an absolute value equation, you need to isolate the absolute value expression on one side of the equation. Then, remove the absolute value bars and create two equations, one with a positive value and one with a negative value. Solve for x in both equations and you will have two solutions for x.
The properties of absolute value are:
Some common mistakes when solving absolute value equations include:
Absolute value is used in various real-life situations, such as calculating distances, measuring errors, determining the magnitude of a force, and finding the difference between two values. It is also used in fields such as physics, engineering, and statistics to represent and analyze data. In everyday life, absolute value can be seen in temperature changes, bank account balances, and sports statistics.