SOLUTION: 3/5X_<-54 -1/3X<-27 please and sooooo many thank yous!

Question 115227: 3/5X_<-54

-1/3X<-27
please and sooooo many thank yous!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#1

Start with the given inequality

Multiply both sides by 5.

Multiply

Divide both sides by 3 to isolate x

Divide

--------------------------------------------------------------
Answer:
So our answer is

Now let's graph the solution set

Start with the given inequality:

Set up a number line:

Now plot the point on the number line

Now pick any test point you want, I'm going to choose x=0, and test the inequality

Plug in

Since this inequality is not true, we simply shade the entire portion that does not contain the point x=0 using the point as the boundary. This means we shade everything to the left of the point like this:
Graph of with the shaded region in blue
note: at the point , there is an closed circle. This means the point is included from the solution set.

#2

Start with the given inequality

Multiply both sides by 3

Multiply

Divide both sides by -1 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)

Divide

--------------------------------------------------------------
Answer:
So our answer is

Now let's graph the solution set

Start with the given inequality:

Set up a number line:

Now plot the point on the number line

Now pick any test point you want, I'm going to choose x=0, and test the inequality

Plug in

Since this inequality is not true, we simply shade the entire portion that does not contain the point x=0 using the point as the boundary. This means we shade everything to the right of the point like this:
Graph of with the shaded region in blue
note: at the point , there is an open circle. This means the point is excluded from the solution set.

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