How do you solve #14<= -x/2#?

1 Answer
EZ as pi
Jun 7, 2016

# x <= -28#

Explanation:

The issue in this example is the fact that the x-term is negative.
In working with inequalities, if you divide or multiply by a negative number, the inequality sign in the middle changes around.
It is better to avoid the problem altogether by moving the x term to the other side. As this is done by ADDING to both sides, there is not a problem.
#14 <= -x/2 " can be changed to " x/2 <= -14#

Now, multiply both sides by 2 to get # x <= -28#

The other method would be as follows:
#14 <= -x/2" multiply both sides by -2"#

#-2 xx 14 >= -x/2 xx-2 " note the sign change in the middle"#
#-28 >= x#
This can be written better as #x <= -28#

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