How do you solve #-1 <= x-3 <= 5#?

2 Answers

Answer:

Solve for #x# by adding #+3# to all three parts of the compound the inequality.

# 2 <= x <=8#

Explanation:

#-1 <= x-3 <-5" " #add 3 to each part

# -1 color(red)(+ 3) <= x -3 color(red)(+ 3) <= 5 color(red)(+3)" "# Doing all of the addition results in

# +2 <= x <= 8" "x # is now isolated in the middle

# 2 <= x <=8" "# this is the final answer

Mar 16, 2017

Answer:

#2 <=x<=8#

Explanation:

#-1 <= x-3 <=5#

You can break the inequality up into two parts, work with them separately, and combine them at the end.

#color(red)(-1 <= x-3 )<=5" "and" " -1 <= color(blue)(x-3 <=5)#

#color(red)(-1 <= x-3 )color(white)(........................................)color(blue)(x-3 <=5)#

Isolate x on the right side #color(white)(................)# isolate x on the left side
#color(red)(-1 +3 <= x )color(white)(........................................)color(blue)(x <=5+3)#

#color(white)(.........)color(red)(2<= x )color(white)(.........................................)color(blue)(x <=8)#

Now combine the two parts with one #x#

#color(white)(...............................)color(red)(2<= )x color(blue)(<=8)#