How do you solve the inequality #-5-x/6> -9#?

First, add #color(red)(5)# to each side of the inequality to isolate the #x# term while keeping the inequality balanaced:

#-5 + color(red)(5) - x/6 > -9 + color(red)(5)#

#0 - x/6 > -4#

#-x/6 > -4#

Now, multiply each side of the inequality by #color(blue)(-6)# to solve for #x# 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)(-6) xx -x/6 color(red)(<) color(blue)(-6) xx -4#

#(color(blue)(6)x)/6 color(red)(<) 24#

#(cancel(color(blue)(6))x)/color(blue)(cancel(color(black)(6))) color(red)(<) 24#

#x < 24#

When working with inequalities it is a good idea to work with a positive variable term. This avoids problems with the inequality sign,

#-5color(blue)(-x/6) > color(red)(-9)#

Move the #color(blue)(-x/6)# term to the right side and the #color(red)(-9)# to the left.

(Add #x/6 and 9# to both sides)

#-5" "color(red)(+9)" "color(blue)(-x/6 +x/6) > color(red)(-9 +9) ""color(blue)(+x/6)#

#" "4 > x/6" "larr ( xx 6)#

#" "24 >x#

This is the same as #x<24#