Question

PLEASE HELP... im super stuck on these 4 problems!!!!
Absolute Values and Inequalities...
1. /x/+5=18
a)5 or -5
b)13 or -13
c)18 or -18
d)23 or -23
2./y+4/<1
a)-5 12 years ago

Answer 1

\(\large {|x|+5=18\implies |x|=18-5\implies
\begin{cases}
+(x)=18-5\\ \quad \\
-(x)=18-5
\end{cases}\\ \quad \\ \quad \\
|y+4|<1\implies
\begin{cases}
+(y+4)<1\\ \quad \\
-(y+4)<1
\end{cases}\\ \quad \\ \quad \\
|2t|-5=7\implies |2t|=7+5\implies
\begin{cases}
+(2t)=7+5\\ \quad \\
-(2t)=7+5
\end{cases}\\ \quad \\ \quad \\
|a|- \cfrac{3}{4}= -\cfrac{5}{8}\implies |a|=-\cfrac{5}{8}+\cfrac{3}{4}\implies
\begin{cases}
+(a)=-\cfrac{5}{8}+\cfrac{3}{4}\\ \quad \\
-(a)=-\cfrac{5}{8}+\cfrac{3}{4}
\end{cases}}\)

Answer 2

I dont understand ...

Answer 3

http://www.youtube.com/watch?v=wE3Us-d5KJo

Answer 4

\[\left| x \right|=a,then x=-a and x=a\]
\[\left| x \right|\le a ,gives -a \le x \le a\]
\[\left| x \right|\ge a,gives x \le -a,x \ge a\]

Answer 5

my computer blocked youtube.com

Answer 6

\[\left| x+a \right|<b,gives -b <x+a <b,subtracting a from each,-b-a<x<b-a\]