How do you solve #-4x-8<=56#?

2 Answers
Aug 10, 2016

#-4x-8<=56#
or
#4x+8>=-56#
or
#4(x+2)>=-56#
or
#x+2>=-56/4#
or
#x+2>=-14#
or
#x>=-14-2#
or
#x>=-16#

Aug 10, 2016

#x>= -16#

Explanation:

Treat an inequality in the same way as an equation, unless you multiply or divide by a negative number, in which case the inequality sign must change around.

We can tackle this question in 2 ways: Compare them.

Make the x-term positive# color(white)(.......................)#keep the x-term on left

#-4x -8 <= 56color(white)(...................................)-4x -8 <= 56#

#-8-56 <= 4xcolor(white)(.........................................)-4x <=56+8#

#-64 <= 4x " "div 4color(white)(....................................)-4x <=64"#

#-16 <= xcolor(white)(..................................................) (-4x)/(-4) color(red)(>=) 64/(-4)#

#x>= -16color(white)(.......................................................)x>= -16#