How do you solve #5- \frac { 1} { 2} k > 0#?

1 Answer
smendyka
Sep 29, 2017

See a solution process below:

Explanation:

First, subtract #color(red)(5)# from each side of the inequality to isolate the #k# term while keeping the inequality balanced:

#-color(red)(5) + 5 - 1/2k > -color(red)(5) + 0#

#0 - 1/2k > -5#

#-1/2k > -5#

Now, multiply each side of the inequality by #color(blue)(-2)# to solve for #k# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

#color(blue)(-2) xx 1/-2k color(red)(<) color(blue)(-2) xx -5#

#cancel(color(blue)(-2)) xx 1/color(blue)(cancel(color(black)(-2)))k color(red)(<) 10#

#1k color(red)(<) 10#

#k color(red)(<) 10#

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