How do you solve and write the following in interval notation: #-5<5+2x<11#?

2 Answers
Alan P. · EZ as pi
Jun 17, 2016

# x in (-5,3)#

Explanation:

You can add/subtract both sides of an inequality without changing the orientation of the inequality;
you can also multiply or divide both (all) sides of an inequality by a value greater than zero without changing the orientation of the inequality..

Given: #-5 < 5 +2x <11

subtract #5# from each "side
#-10 < 2x < 6#

divide each "side" by #2#
#-5 < x < 3#

EZ as pi
Jun 17, 2016

#-5 < x < 3# or in interval notation: #x in (-5, 3)#

Explanation:

Break the question into two inequalities and solve each separately.

LHS: keep x term on the right but on the RHS keep x term on left

#-5 < 5 + 2x " and " 5 + 2x <11#

#-5 -5 < 2x " " 2x < 11-5#

#-10 <2x " " 2x < 6#

#-5 < x " " x < 3#

But the x terms are the same term, so the two parts can be combined:

#-5 < x < 3#

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