How do you solve and graph #-6(w + 1) < 2(w + 5) #?

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Answer 1 · 2018-07-21T21:17:03

#w > -2#

#-6(w+1) < 2(w+5)#

Simplify each side by distributing:
#-6w - 6 < 2w + 10#

Add #color(blue)(6w)# to both sides of the inequality:
#-6w - 6 quadcolor(blue)(+quad6w) < 2w + 10 quadcolor(blue)(+quad6w)#

#-6 < 8w + 10#

Subtract #color(blue)10# from both sides:
#-6 quadcolor(blue)(-quad10) < 8w + 10 quadcolor(blue)(-quad10)#

#-16 < 8w#

Divide both sides by #color(blue)8#:
#(-16)/color(blue)8 < (8w)/color(blue)8#

#-2 < w#

#w > -2#

This can be said as "#w# is greater than #-2#."

Here's a graph of it on a number line:
enter image source here
(mathwarehouse.com)

The open circle means that #-2# is not one of the solutions.

Hope this helps!