SOLUTION: The following is my question: -2 + |x| + 9 = 10 Could you please help? Thank you! Jesse

Algebra ->  Systems-of-equations -> SOLUTION: The following is my question: -2 + |x| + 9 = 10 Could you please help? Thank you! Jesse      Log On


   

Question 936430: The following is my question: -2 + |x| + 9 = 10
Could you please help?
Thank you!
Jesse
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+-2+%2B+abs%28+x+%29+%2B+9+=+10+
+abs%28+x+%29+%2B+7+=+10+
Subtract +7+ from both sides
----------------------------
+abs%28+x+%29+=+3+
The absolute value is always positive
because
+abs%28+x+%29+=+abs%28+-x+%29+
So,
+x+=+3+
+x+=+-3+
are both solutions
--------------------
I can demonstrate this by plotting
+y+=+abs%28x%29+
+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+6%2C+abs%28x%29+%29+
Note that when +x+=+3+, +y+=+3+
but also when +x+=+-3+, +y+=+3+