How do you solve and write the following in interval notation: #2x - 4< 4# or# x + 5 ≤ 2 - 2x#?

1 Answer
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

1
ASAP Share
Oct 20, 2017

Answer:

  1. #x<4# and in interval notation # x in(-oo,4)#
  2. #x<=-1# and in interval notation #x in(-oo,-1]#

Explanation:

Lets take the first example.

#2x-4<4#

This is an inequality. Inequalities are usually solved like regular equations.

Lets add #4# to both sides of the equation.

#2x-4+color(red)4<4+color(red)4#

#2x<color(red)8#

Divide both sides by #2#

#(2x)/color(red)2<8/color(red)2#

#x<4#

This inequality means that the value of #x# has to be less than #4# to satisfy the inequality.

In interval notation it will be written as # x in(-oo,4)# because the value of #x# can be any number between #-oo# and #4# but cannot be #-oo# or #4# hence we use this ( ) bracket.

Similarly when we simplify #x+5<=2-2x# we get #x<=-1#

So here the interval notation is #x in(-oo,-1]# because #x# can be any number between #-oo# and #-1# and can be #-1# but cannot be #-oo# hence this ( ] bracket.

Was this helpful? Let the contributor know!
1500
Impact of this question
Answer impact map
16 views around the world
You can reuse this answer
Creative Commons License