How do you solve the inequality #-15 <= c/-4 - 15#?

1 Answer
Júlio B.
Jan 1, 2016

The solution set is: #S = {c in RR | c <=0}#

Explanation:

In this specific case, we first make the inequality easier, simplifying it:
# -15 <= c/-4 -15 # multiply it by 4: #-60 <= c/-1 -60#
#c/-1 = -c#. So, we pass the #-60# to the other side of the inequality and solve it:

#-60 + 60 <= -c#
# 0 <= -c#

In order to make the #c# to be positive, just multiply it by -1. But, when this is made, the inequality signal is reversed - If it is #<#, becomes #>#, etc. Now, in this case:

# 0 <= -c# multiplied by #-1#:
# 0 >= c#
# c <= 0#

So, the solution set is: #S = {c in RR | c <=0}#

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