Question #d3c3a

1 Answer
Dec 21, 2017

#color(blue)(y<2x# and

#color(blue)(y > (6-2x)/3)#

Explanation:

We have two inequality expressions:

First expression is

#color(blue)(y<2x#

This inequality expression is already in simplified form.

Next expression is

#color(blue)(2x+3y>6)#

We can simplify this expression by subtracting #color(red)(2x)# from both sides of the inequality.

#rArr 2x+3y-2x>6-2x#

In the next step we can cancel

#rArr cancel(2x)+3y cancel(-2x)>6-2x#

Hence, we get

#rArr 3y >6-2x#

Divide both sides of the inequality as shown below:

#rArr (3y)/3 >(6-2x)/3#

In the next step we can cancel

#rArr (cancel(3)y)/cancel 3 >(6-2x)/3#

Hence, our solution is

#rArr y >(6-2x)/3#

Hence we have two solutions

#color(blue)(y<2x# and

#color(blue)(y > (6-2x)/3)#

Please refer to the graphs below:

#color(blue)(y<2x#

enter image source here

Next expression is

#color(blue)(2x+3y>6)#

enter image source here

Our simplified expression is

#color(blue)(y > (6-2x)/3)#

enter image source here

We observe that the last two graphs represent the same inequality.

Hope this helps.