0Lucky0 wrote:
Q.: |x+3|−|4−x|=|8+x|. How many solutions does the equation have?
KarishmaB, I have read all 6 pages on here looking for your explanations but I can't seem to find a post where you solve this question using your patented number line technique.
I also read all 3 pages of explanations on the original question post, even there you don't actually answer this question anywhere using that technique.
You did answer a loooooot of questions on this and explained stuff using both the number line and without the number line but I couldn't find a post where you by yourself answer this question using the method you would prefer.
This Modulus topic is an extremely complicated topic and I really don't wanna read anyone else's explanations but yours as IMO, you are a master at this; also because reading too much of this is just frying my brain.
So if possible, please answer this question using your patented number line method in one post.
Thank you sooo much..
You truly are a genius.
I am guessing that the link shared by Bunuel would have already helped you but since you took the time to write those kind words
here is the straight and simple method of doing the question my way:
|x+3|−|4−x|=|8+x|
Re-write as:
|x+3| = |x+8| + |x - 4|
(because sum of distances is easier to handle than difference of distances)
Draw the transition points on the number line:
------------------- (-8) ----------- (-3) --------------------------- (4) -------------
Now I will think, where on this number line will the distance from -3 be equal to sum of distances from -8 and 4.
At the part to the left of -8? No. 4 is farther off than -3.
At the part between -8 and -3? No. 4 is farther off than -3.
At the part between -3 and 4? No. -8 is farther off than -3.
At the part to the right of 4? No. -8 is farther off than -3.
Hence there is no region and no point where the distance from -3 is equal to sum of distances from -8 and 4.
Answer (A)
If you are unsure of how absolute values are taken as distances, I have a YouTube video on it here:
https://youtu.be/oqVfKQBcnrsThe channel is work in progress so I have been hesitant to share it as of now, but the video explains the concept the way I wish to, so go ahead!