SOLUTION: Solve and give answer in interval notation {{{(x+5)(3x-4)>0}}}

Question 135369: Solve and give answer in interval notation

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given inequality

Set the left side equal to zero

Solve for x in each case

So this means that the critical values are

Now plot the critical values on a number line

So let's evaluate a point that is to the left of

(which is the left most endpoint). Let's evaluate the value

Start with the given inequality

Plug in

Evaluate and simplify

Since

is true, this means that everything to the left of is in the solution set. So the graph looks like this

So one part of the solution in interval notation is

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Now let's test a point that is in between the critical values

and

Start with the given inequality

Plug in

Evaluate and simplify

Since

is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored.
-----------------------------------------------

So let's evaluate a point that is to the right of

(which is the right most endpoint). Let's evaluate the value

Start with the given inequality

Plug in

Evaluate and simplify

So everything to the right of

is in the solution set. So our graph now looks like

Since

is true, this means that one part of the solution in interval notation is

-----------------------------------------------

Answer:

So the solution in interval notation is

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