How do you solve and graph #-2b + 4 > -6 #?

1 Answer
smendyka
Aug 28, 2017

See a solution process below:

Explanation:

First, subtract #color(red)(4)# from each side of the inequality to isolate the #b# term while keeping the inequality balanced:

#-2b + 4 - color(red)(4) > -6 - color(red)(4)#

#-2b + 0 > -10#

#-2b > -10#

Now, divide each side of the inequality by #color(blue)(-2)# to solve for #b#. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

#(-2b)/color(blue)(-2) color(red)(<) (-10)/color(blue)(-2)#

#(color(red)(cancel(color(black)(-2)))b)/cancel(color(blue)(-2)) color(red)(<) 5#

#b < 5#

To graph this inequality we will draw a vertical line at #5# on the horizontal axis.

The line will be a dashed line because the inequality does not contain an "or equal to" clause.

We will shade to the left of the dashed line because the inequality operator contains a "less than" operator:

graph{x < 5}

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