SOLUTION: Solve the inequality: 8x^2<9-x

Algebra ->  Inequalities -> SOLUTION: Solve the inequality: 8x^2<9-x      Log On


   

Question 737211: Solve the inequality: 8x^2<9-x
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
-9/8 x ranges from -9/8 to 1

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
8x^2<9-x
------
8x^2 + x - 9 < 0
-----
8x^2 + 9x - 8x -9 < 0
-----
x(8x+9) - (8x+9) < 0
----
(8x+9)(x-1) < 0
-----
Draw a number line: plot x = -9/8 and x = 1
---
Test 3 intervals for solutions:
Let x = -10 to get: -*- < 0 :::: false
Let x = 0 to get::: +*- < 0 :::: true
Let x = 10 to get:: +*+ < 0 :::: false
----
Conclusion:
-9/3 < x < 1 is the solution set
==========================
Cheers,
Stan H.
==========================