How do you solve #-6( 8+ 4a ) > 32- 8a#?

1 Answer
seol
Sep 6, 2017

#a\lt-4.625#

Explanation:

#\color(seagreen)(-6(8+4a))\gt32-8a#
#\color(seagreen)(-6(8)+(-6)(4a))\gt32-8a# distributive property
#\color(seagreen)(-42+(-24a))\gt32-8a# simplify
#-42-24a\gt32-8a# change signs where needed

#\color(slateblue)(8a)-42-\color(slateblue)(24a)\gt32# move all variable terms to left side
#\color(slateblue)(-16a)-42\gt32# simplify

#-16a\gt\color(indianred)(32+42)# move non variable terms to right side
#-16a\gt\color(indianred)(74)# simplify

#a\lt74/(-16)# divide to isolate variable (if you divide by a negative number, you change the direction of the inequality)

#a\lt-4.625# simplify

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