How do you solve the graph: 1<3x-2≤10?

1 Answer
Alan P.
Oct 2, 2015

#1 < x <= 4#
as a line graph:
enter image source here

Explanation:

Given an inequality, you can
- add the same amount to both sides
- divide both sides by any amount greater than zero
without effecting the validity or orientation of the inequality

#1 < 3x-2 <=10#

can be split into two inequalities

#1 < 3x-2#
#color(white)("XXX")rarr 3 < 3x#
#color(white)("XXX")rarr 1 < x#

and

#3x-2 <= 10#
#color(white)("XXX")rarr 3x <= 12#
#color(white)("XXX")rarr x <= 4#

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