SOLUTION: How would I solve these inequalities by factoring and making appropriate sign charts? 1. x^2 - 3x >= 10 or 2. x^3 + 4x^2 - x >= 4 or 3. 2sin^2(x)>= sinx , 0<=z<=2pi

Question 638427: How would I solve these inequalities by factoring and making appropriate sign charts?
1. x^2 - 3x >= 10
or
2. x^3 + 4x^2 - x >= 4
or
3. 2sin^2(x)>= sinx , 0<=z<=2pi
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve these inequalities by factoring and making appropriate sign charts?
1. x^2 - 3x >= 10
x^2-3x-10 >= 0
Factor:
(x-5)(x+2)>= 0
---
Draw a number line ; plot x = -2 and x = 5
If x<-2 the product is > 0
If -2< x <5 the product is < 0
If x > 5 the product is > 0
----
Solution: (-oo,-2]U[5,+oo)
===============================
or
2. x^3 + 4x^2 - x >= 4
x^3+4x^2-x-4 >=0
x^2(x+4)-(x+4)>= 0
(x+4)(x^2-1)>=0
(x-1)(x+1)(x+4) >= 0
Draw a number line ; plot x = -4, x = -1, x = +1
---
Find the solution intervals.
=====================================
or
3. 2sin^2(x)>= sinx , 0<=z<=2pi
2sin^2(x)-sin(x) >= 0
sin(x)(2sin(x)-1) >= 0
sin(x) = 0 , sin(x) = 1/2
Draw a number line ; plot x = 0, x = pi/6, x = (5/6)pi, x = 2pi
----
Find the solution intervals.
=================================
Cheers,
Stan H.
=================

RELATED QUESTIONS
Solve the following by factoring and making appropriate sign charts:... (answered by stanbon)

Solve the equation by making an appropriate substitution.... (answered by stanbon)

x^4-3x^2-10=0 solve by making the appropriate... (answered by rapaljer)

I need to rewrite without absolute value sign; |x-2|-2|3x-12|,|x-10|-2|2x+4|+3|4x-4|,... (answered by stanbon)

How would I use the p over q method and synthetic division to factor these polynomials... (answered by tinbar)

How would I simplify and state the non-permissible values of these questions?... (answered by stanbon,Edwin McCravy)

Hello. Here are three problems involving the Quadratic Equation that I am having trouble (answered by ramkikk66)

I have to solve this equation by making appropriate substitutions: x^4- 9x^2 =... (answered by fcabanski)