SOLUTION: Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 5x^2-3x is greater than or equal to 8

Question 156261: Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation.
5x^2-3x is greater than or equal to 8
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Express the solution set in interval notation.
5x^2-3x is greater than or equal to 8
---------------------------------------
5x^2 - 3x -8 >= 0
5x^2 -8x+5x -8 >= 0
x(5x-8) +(5x-8)
(5x-8)(x+1) >= 0
----------------------
Solve the EQUALITY:
x = 8/5 or x = -1
----------------------
Draw a number line: plot -1 and 8/5 on it.
Check a test point from each resulting numberline interval in the INEQUALITY.
Let x = -2; you get 5(-2)^2-3*-2-8 >0; true; solutions in (-inf,-1)
----------------------
Let x = 0; you get 5*0 - 3*0 -8 > 0 ; false; no solutions in (-inf,1)
-----------------------
Let x = 2; you get 5(2)^2-3*2-8 >0 ; true; solutions in (8/5,+inf)
------------------------
Final Answer: {x| x<=-1} U {x|x >= 8/5}
===========================

===========================
Cheers,
Stan H.

RELATED QUESTIONS
solve the polynomial inequality and graph the solution set on a real number line. Express (answered by robertb)

Solve the polynomial inequality and graph the solution set on a number line. Express the... (answered by lwsshak3)

Solve the polynomial inequality and graph the solution set on a real number line. Express (answered by lwsshak3)

solve the rational inequality and graph the solution set on a real number line. Express... (answered by oscargut)

Solve the rational inequality and graph the solution set on a real number line. Express... (answered by stanbon)

solve the polynomial inequality and graph the solution set on a number line. express the (answered by oscargut)

solve the compound inequality. other than 0 use interval notation to express the... (answered by jim_thompson5910)

Solve the compound inequality. Other than 0 use interval notation to express the... (answered by jim_thompson5910)