Algebra help?

Question

Solve each inequality:
x2 - 7x + 12 < 0

3x2 + 5X -12 > 0

3x2 - 5x -12 <_ 0

How would I solve these? The numbers after the "x"s in all 3 questions are exponents. The last question is Greater Than or Equal to Zero. How do I figure these out?

Answer 1

I won't give you the answers, but I will tell you the basics to solving the inequalities

First, set all the equations equal to zero. Then, solve the equations. After finding the roots, draw a number line showing the smaller root and the larger root, and choose a number less than the smaller root, a number between the roots, and a number larger than the larger root. Plug in the numbers separately into each of the three equations. If the numbers closest to the roots satisfy the equation, then shade outward, away from the roots. If the two numbers closest to the roots don't satisfy the equation, then shade inward. The inward shaded answer would be something like {root
Also another note: less than/greater than are open circles, and less than or equal to/greater than or equal to are closed circles.

I hope this helps. If you have any questions, ask your math teacher for more help.

Answer 2

Factor each first and then find the significant numbers.

(x+3)(x+4) < 0 .......... -3 and -4 are significant since x cannot = 3 or 4 as it would cause the equation to EQUAL zero. Then divide a number line with breaks at these numbers.


* -4 * -3 *
<------------------------------------------>


Pick number from each region to see if they satisfy the inequality

x = -5 and x = -3.5 and x = -2

no : yes : no

Therefore x is between and not including -3 and -4

Answer 3

You need to factor each expression. The first one, for example, is
(x-3)(x-4)<0
x=3,4

Good luck.

Answer 4

x² - 7x + 12 < 0

x² - 4x - 3x + 12 < 0

x(x - 4) - 3(x - 4) < 0

(x - 3)(x - 4) < 0

- - - - - - - - - - -s-

Answer 5

just plug in any number for x