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I have this humungous equation:

|x + 3| - 2|x + 1| - |x + 1| - |x - 1| + 2|x - 2| = 4 - 2x

I have tried to use the snake method/interval method to solve this problem, but I failed to get all of the solutions. This is what I have tried:

https://mega.nz/#!SqBGzAxA!e7zwPu46IhqcCam04w6Aw4nObgPJcx0FAHLjNGxS4KE (I don't have enough reputation to post direct links to images of my work, so this is a shortened link)

Anyone know how to solve such a large equation?

Brandon Li
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  • Welcome to MSE. Please don't post images when you can type the work, as in this case. Images can't be browsed, and aren't accessible to those using screen readers. In this case, I couldn't access your link unless I created an account, which I don't care to do. Just show us your work, or enough of it to indicate your method. What in the world is the "snake method"? – saulspatz Oct 14 '19 at 03:50
  • The formula above, and the formula in the picture do not match – Andrei Oct 14 '19 at 03:55

2 Answers2

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I would consider points of interest to be the boundary points. $$ x= -3,-1,1,2$$

Partition the real line like $$(-\infty,-3)\cup (-3,-1)\cup (-1,1)\cup (1,2)\cup (2,\infty)$$

For the boundary points $x=-1$ is a solution. For the interior points you need to get rid of ab solute values and solve. Check for consistency and pick solutions if any.

Mohammad Riazi-Kermani
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Do cases.

Case 1: $x+3 < 0$

Case 2: $x+ 3 \ge 0$ but $x+1 < 0$.

Case 3: $x+1 \ge 0$ but $x-1 < 0$.

Case 4: $x-1 \ge 0$ but $x -2 < 0$.

Case 5: $x-2 \ge 0$.

.....

fleablood
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