absolute values are SCArY!!!

jazzyredsox5 · #1 $Old$ August 26th, 2009, 07:46 PM

i understand that an absolute value is the distance on a number line from zero, and that abs(y)=8 would be 8, -8, but when it gets to like abs(c/4)=9, i know you have to make two equations, c/4=9 and c/4=-9, because my sheet says so, but why? i don't understand why the 9 is affected when it is not in the absolute value bars.......

pickslides · #2 $Old$ August 26th, 2009, 07:59 PM

By definition $|a|\leq b \Rightarrow -b \leq a \leq b$

Why?

Look at the function $y = |x|$

jazzyredsox5 · #3 $Old$ August 26th, 2009, 08:12 PM

[quote=pickslides;355065]By definition $|a|\leq b \Rightarrow -b \leq a \leq b$

i was never taught absolute value by that equation before... so if abs(w-8)=7, then would i set up the equation to be w-8=16 and w-8=-16 and then solve?

pickslides · #4 $Old$ August 26th, 2009, 08:26 PM

Quote:

Originally Posted by jazzyredsox5 $View Post$

so if abs(w-8)=7, then would i set up the equation to be w-8=16 and w-8=-16 and then solve?

So what are you asking? I am confused how 7 can be equal to 16?

I'm guessing you are saying $|w-8|\leq 7 \Rightarrow -7 \leq w-8 \leq 7$

Therefore solve both

$-7 \leq w-8$

$1 \leq w$

$w \geq 1$

and

$w-8 \leq 7$

$w \leq 15$