SOLUTION: what is the inequalities of algebraically is like x^2-2x-15

SOLUTION: what is the inequalities of algebraically is like x^2-2x-15 < 0?

Question 175272This question is from textbook algebra 2
: what is the inequalities of algebraically is like x^2-2x-15 < 0? This question is from textbook algebra 2

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

Start with the given inequality

Factor the left side

Set the left side equal to zero

Set each individual factor equal to zero:

or

Solve for x in each case:

or

So our critical values are and

Now set up a number line and plot the critical values on the number line

So let's pick some test points that are near the critical values and evaluate them.

Let's pick a test value that is less than (notice how it's to the left of the leftmost endpoint):

So let's pick

Start with the given inequality

Plug in

Evaluate and simplify the left side

Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it.

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

Let's pick a test value that is in between and :

So let's pick

Start with the given inequality

Plug in

Evaluate and simplify the left side

Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.
So part our solution in interval notation is (

)

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

Let's pick a test value that is greater than (notice how it's to the right of the rightmost endpoint):

So let's pick

Start with the given inequality

Plug in

Evaluate and simplify the left side

Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it.

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

Answer:

So the solution is

So the solution in interval notation is:

(

)

RELATED QUESTIONS
What is the inequalities of -2x >... (answered by MathLover1)

When x^2-2x+1>0, what does zero in this inequalities mean? is x^2-2x+1 the... (answered by josgarithmetic)

Solve the system algebraically. 2x + y - 10 = 0 x - y - 5 = 0 What is the value of (answered by mananth)

"what is the value of x?" 2x� + 12x + 15 = 0 (answered by AnlytcPhil)

what is the values of x so that... (answered by checkley77)

Alright, so I'm supposed to solve this equation algebraically, but I'm not sure what the... (answered by ankor@dixie-net.com)

Solve the following system of equations algebraically and check: y = 2x^2 + 2x + 3 x =... (answered by Fombitz)

compound inequalities I really need someone to work this one out with all the steps so I (answered by solver91311)

Solve the equation algebraically.... (answered by jim_thompson5910)