How do you solve abs(6-x)=9?

2 Answers
İnci
Sep 29, 2015

Remember the rule:
|x|=a
If x<0
a_1= -x
If x>0
a_2=x
So if x's interval isn't determined we will have 2 results.

Explanation:

6-x>0

|6-x|=6-x
6-x=9
x_1=-3

6-x<0

|6-x|=x-6
x-6=9
x_2=15

Ken C.
Sep 29, 2015

x = 15 and x = -3.

Explanation:

Absolute value equations have two solutions; since absolute values will always be positive, this makes sense. For example, in abs(x) = 9, x can equal 9 and -9; the absolute value of 9 equals 9 and the absolute value of -9 equals 9.

As such, we need two equations to find the two solutions. Our two equations are: 6-x = 9 and 6-x = -9. You've probably noticed that these equations are extremely similar - except one equation equals 9, and the other -9. Always set up absolute value equations like this when you're ready to solve.

Let's get to the solving, starting with 6-x = 9:

6-x = 9 (original equation)
-x = 3 (subtracting 6 from both sides)
x = -3 (dividing by -1)

Alright, x = -3 is one solution. Now, for 6-x = -9:

6-x = -9 (original equation)
-x = -15 (subtracting 6 from both sides)
x = 15 (dividing by -1)

And that's it. Our solutions are x = 15 and x = -3.

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