## Challenge 343: Modulus Mystery

*Information for this problem:*

The notation | x | means the **modulus **of x, which is just the “size” of x.

So if x = -5, then | x | = 5, and if x = 4.2, then | x | = 4.2.

We can also find the modulus of an expression.

For example, if x = -2, | x^{2} + x – 3 | = | 4 - 2 - 3 | = | -1 | = 1

**Here’s the problem:**

Find all values of x for which | x + 1 | + | x^{2} + 4x + 3 | = 12

Explain how you know you have found all the possible values.

### Submit your solution

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