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

Question

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

Kennedy Adams · Accepted Answer

#p\lt2# 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!

Avery Alexander · Answer

#p <2#

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#

Kennedy Adams · Answer

undefined To solve -p-4p > -10, combine like terms on the left side to get -5p > -10. Then, divide both sides by -5, remembering to flip the inequality sign when dividing by a negative number, to get p < 2.

How do you solve #-p-4p&gt; -10#?

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