How do you solve 2x - 1 > 5 and 3x < - 6?

1 Answer
Jim H
Jul 6, 2015

The compound inequality has no solution.

Explanation:

This is a Compound Inequality.

In order to solve an inequality that involves the word "and", we must find values of #x# that make the inequalities true at the same time. (To solve a compound inequality with "or" we need to find values of #x# that make at least one of the inequalities true.)

The problem asks us to solve:
#2x-1 > 5 " and " 3x < -6#

In order to satisfy: #2x-1 > 5# we need:

#2x > 6# so #x>3#

In order to satisfy: #3x < -6# we need:

#x < -2#

In order to satisfy the compound inequality:
#2x-1 > 5 " and " 3x < -6#

we need an #x# that satisfies both:

#x > 3 # and the same #x# satisfies #x < -2#. There is no such #x#.

It may help to think of the number line. We need a number #x# that is to the right of #3# and the same number if to the left of #-2#. No such number exists.

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