How do you solve and graph #-2/3f+3<-9#?

1 Answer
Oct 2, 2017

Answer:

See a solution process below:

Explanation:

First, subtract #color(red)(3)# from each side of the inequality to isolate the #f# term while keeping the inequality balanced:

#-2/3f + 3 - color(red)(3) < -9 - 3#

#-2/3f + 0 < -12#

#-2/3f < -12#

Now, multiply each side of the inequality by #color(blue)(3)/color(orange)(-2)# to solve for #f# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality sign.

#color(blue)(3)/color(orange)(-2) xx (-2)/3f color(red)(>) color(blue)(3)/color(orange)(-2) xx -12#

#cancel(color(blue)(3))/cancel(color(orange)(-2)) xx color(orange)(cancel(color(black)(-2)))/color(blue)(cancel(color(black)(3)))f color(red)(>) color(blue)(3)/cancel(color(orange)(-2)) xx color(orange)(cancel(color(black)(-12)))6#

#f color(red)(>) color(blue)(3) xx 6#

#f color(red)(>) 18#

To graph this we will draw a vertical line at #18# on the horizontal axis.

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

We will shade to the right side of the line because the inequality operator also contains a "greater than" clause:

graph{x>18 [-10, 30, -10, 10]}