# Core 3 - Modulus: Solve the equation |x-2|=|x+6|.

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Modulus, also known as absolute value, takes whatever's between the |straight brackets| and makes it positive. For example, |3|=3, and |-3|=3. Interestingly, if you have any real number x, then |x|=sqrt(x2). Try putting some numbers in and see!

We can't solve a modulus question until we get rid of the straight brackets, but this little trick will do the job every time. If we square both sides of the modulus equation in the last paragraph, we get |x|2=x2. So modulus brackets disappear when we square both sides of our equation. Let's try it...

|x-2|2=|x+6|2

(x-2)2=(x+6)2

x2-4x+4=x2+12x+36

-16x=32

x=-2

This trick is great, because the xterms cancel out and there's no quadratic equation to mess about with. Beware though, this will not be the case in all questions - if you get a quadratic equation to solve, you may end up with more than one solution. Try these bonus questions and see for yourself:

(1) Solve the equation |x+4|=|x-5|.​

(2) Solve the equation |x-3|=|2x|.​

(3) Solve the equation |3x-1|=|3-x|.​

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