How can I solve this inequality problem involving factoring?

[brwneyes02]

Homework Statement

Solve the inequality

(2x-3)(4x+5)>(x+6)(x+6)

Homework Equations

factoring?

The Attempt at a Solution

I got to the point where

(7x)^2-14x-51>0 I can't solve this, because it can't be factored out. So am I doing something wrong?

 

[symbolipoint]

Good work reaching that quadratic inequality. It would be related to a parabola opening upward. Look for the critical points. Does this have no roots, one root, or two roots? Which intervals make the quadratic inequality true?

For critical points, remember the general solution to a quadratic equation, or can you factor the expression?
EDIT: In fact, you're right. 7x^2-14x-51 is not factorable. Use either completing the square, or the solution to a quadratic equation.

 

[HallsofIvy]

Homework Statement

Solve the inequality

(2x-3)(4x+5)>(x+6)(x+6)

Homework Equations

factoring?

The Attempt at a Solution

I got to the point where

(7x)^2-14x-51>0 I can't solve this, because it can't be factored out. So am I doing something wrong?

Well, first, it is NOT (7x)^2, it is 7x^2. As symbolipoint suggested, complete the square or use the quadratic formula to determine the values of x at which 7x^2- 14x- 51= 0. Since the graph of this function is a parabola opening upward, the values of x satisfying the inequality will be less than the lower of the two zeros and larger than the larger. The values of x between the zeros satify "< 0".

 

[brwneyes02]

okay, using quadratic formula I got

x=7+/- sq root of 406 all over 7

(sorry I'm not sure how to write this to make since any other way.)

is this correct?

 

[HallsofIvy]

Yes, those are the solutions to the quadratic equation. Now, what are the solutions to the inequality?

 

[brwneyes02]

how do i do that?

is it
.00000004? one of them? we haven't had this in class. I'm thinking she wrote this problem wrong.

 

[symbolipoint]

You may be more successful in fully managing the solution if you just study the parts from the book to fill-in the topics that your teacher has not yet shown you in class.

 

[HallsofIvy]

I already told you how to do that:

Since the graph of this function is a parabola opening upward, the values of x satisfying the inequality will be less than the lower of the two zeros and larger than the larger. The values of x between the zeros satify "< 0".

No, this problem is perfectly solvable. You have already done most of the work. Do you understand that inequalities typically have not a single solution, but a range of solutions?