How do you solve and write the following in interval notation: #2x − 1 < x + 6 <3x − 4 #?

1 Answer
Jumbotron
Oct 27, 2017

#7 > x > 5#

Explanation:

#2x - 1 < x + 6 < 3x - 4#

We will divide the equations into two parts!

#2x - 1 < x + 6 and x + 6 < 3x - 4#

Solving the First Part!

#2x - 1 < x + 6#

Subtract #x# from both sides..

#2x - 1 - x < x + 6 - x#

#2x - x - 1 < x - x + 6#

#x - 1 < 0 + 6#

#x - 1 < 6#

Add #1# to both sides

#x - 1 + 1 < 6 + 1#

#x + 0 < 7#

#x < 7#

Same as #7 > x#

Solving the Second Part!

#x + 6 < 3x - 4#

Subtract #x# from both sides..

#x + 6 - x < 3x - 4 - x#

#x - x + 6 < 3x - x - 4#

#0 + 6 < 2x - 4#

#6 < 2x - 4#

Add #4# to both sides..

#6 + 4 < 2x - 4 + 4#

#10 < 2x + 0#

#10 <2x#

Divide both sides by #2#

#10/2 < (2x)/2#

#10/2 < (cancel2x)/cancel2#

#10/2 < x#

#5 < x#

Same as #x > 5#

Hence adding both..

#7 > x > 5#

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