How do you solve #-p-4p> -10#?

equation
#-p-4p\gt-10#

concepts applied
if #-a(b)\gtc#, then #b\color(red)(\lt)c/-a#

calculation
add like terms #rArr -5p\gt-10#
divide both sides by -5 #rArr(\cancel(-5)p)/\cancel(\color(olive)(-5))\color(red)(\lt)(-10)/\color(olive)(-5)#
simplify division #rArrp\lt2#

checking
plug in any value less than 2
#-(1)-4(1)\stackrel{?}{\gt}-10#
#-1-4\stackrel{?}{\gt}-10#
#-5\gt-10#
correct!

You can treat an inequality in the same way as an equation, unless to multiply or divide by a negative number, in which case the inequality sign will change around.

Let's swop the negative terms onto the other sides.

#-p -4p > -10" "larr# simplify the like terms

#-5p > -10" "larr# Add 5p to both sides

#-5p +5p > -10 +5p" "larr# add 10 to both sides

#10 > 5p" "larr div 5 #

#2 > p" "larr# this means the same as:

#p < 2#

Note that the same result would have been obtained by dividing by #-5# and changing the inequality sign, as explained by another contributor.

#-5p > -10#

#(-5p)/-5 < (-10)/-5" "larr# note the sign changes!

#p < 2#