Absolute Value As Distance To Zero
November 22nd, 2006 | by christine |Remember Danica McKeller of “Wonder World” fame?
She has a PhD in mathematics now. She loves math so much, that she answers math questions on her blog.
For example:
Q: Hi Danica, I’ve always had problems solving “absolute value” equations. Can you help me by doing one? How about |2x+6| = 10, and we have to “solve for x”. Thanks!
Danica Answers: To find all the “x” values that satisfy your equation, we must solve two separate equations:
2x+6 = 10 and
2x+6 = -10
Do you see why? If the absolute value of a quantity must equal “something” (in this case, 10), then that quantity inside the absolute value signs can either be equal to that positive something, or to the negative of that “something,” and the absolute value of it will always be that “positive something.” So if the inside of the absolute value signs equals -10, the absolute value of it will still be positive 10.
So we just solve the above two equations with basic algebra and we get that x can equal 2 or -8, and both will satisfy |2x+6| = 10. As always, plug your final answers into the original equation to check your work. I like to think of absolute value as “the distance to zero” from whatever’s inside. Hope that helps!
Cool.
To get to the mathematics section on Danica’s site, visit http://www.danicamckellar.com/ and select “mathematics” on the left nav.
