How do you graph the inequality #6(y+1)< -x#?

1 Answer
May 30, 2016

Supporting Brian's solution

Just another way of showing the inequality and a tip about method.

Explanation:

#color(brown)("You can manipulate an inequality the same way you do an equation.")# Just be mindful of this (by example and using numbers to make my point), suppose we had
# -3< 4#

If we multiply by #(-1)# but do not change the inequality we have

#+3<-4 color(red)(" This is false!")#

Be mindful of what the inequality is doing.

We should have had: #(-1)(-3<4) -> color(green)(3 > -4 )#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Solving your question")#

Given:

#6y+6<-x#

Subtract 6 from both sides

#6y<-x-6#

Divide both sides by 6

#6/6 y<-x/6-1#

But #6/6=1#

#y<-x/6-1#

Tony B