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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, | x2 + x – 3 | = | 4 - 2 - 3 | = | -1 | = 1

 

Here’s the problem:

Find all values of x for which | x + 1 | + | x2 + 4x + 3 | = 12

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

Submit your solution

Please do send in your solution to this problem to  weeklymaths@kcl.ac.uk  You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.