Simplify: (a) |6 − x| + |x − 10| if |4 − x| = 4 − x and |2 − x| = x − 2.

(b) Simplify 2 − |2 − |x − 2|| if x < −2.

(c) Evaluate a^2− 2ab if |a − 2| + |3 + b| = 0

(d) Find all possible values of y for which |2y + 7| = |3y − 1|.

(a) 16-2x

(b)-x-2 or x+6

(c)

Step-by-step explanation:

(a)

|6-x|+|x-10|,

|4-x|=4-x,so x<4

|2-x|=x-2=-(2-x)

2-x<0

2<x

or x>2

2<x<4

so |6-x|=6-x,in 2<x<4

|x-10|=-(x-10),in 2<x<4

|6-x|+|x-10|=6-x-(x-10)=6-x-x+10=16-2x

(b)

2-|2-|x-2||,if x<-2

|x-2|=-(x-2) if x<-2

=2-|2-{-(x-2)}|

=2-|2+x+2|

x<-2

x+2<0

=2-|x+4|

=2-(x+4),if x>-4,or -4<x<-2

=2-x-4

=-x-2

if x<-4

then |x+4|=-(x+4)

2-|x+4|=2-{-(x+4)}

=2+x+4

=x+6

take the top number and divide it by a the bottom number

step-by-step explanation:

1/2 1 divied by 2 = .5

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.