Question

Solve the following inequality. (x+2)(x-3)(x+8)>0Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".

Answer 1

than zero, there Griven inequality is (x+2)(x+3)(x+8) >0. For this to be four possibilities. Case ir (x+2)30, (x -3) >0, (x+8)>0 greater are а 6c50 +++ 4 Conditi ons + -- + - 7 » 23-2, x3, x>-8 22-8 xx-2 X>3 4 5 6 7 8 D 1 2 3 -8-7 6-5 -4 -3 -2 -1 .. the Common Solution, solution x3 works for the inequality x>3] is one of solutions above Case ir (x+2)>0, (x-3) 20, (x+8) <0 x<-8 x 3-2, x<3, x<3 s x>-2 XC-8 1 2 3 4 5 -8-76-5-4-3-2-10 No common solution,

interval that Hence there is no satisfies these requirements, Case ill, (x+2)<o, (x-3) 50, (x+8) co xc-2, x33, xc-8 xc-2 a> 3 ac -8 E -8-7-6 5-4-3-2-1 1 3. 5 No interval that satisfies three inequalities Case ju, r (x+2) <0, (x-3) <0, (x+8)) <-2, U23, xs-8 1x3-8 a<3 x<- 1 2 3 4 5 6 7 8 87.6-5-4-3-2 - 0 case. Common Solution : The Inequality x>-8 and ac-2 satisfies the above 18<a<-2 I is one .. from all 4 cases, the final solution is {x>3}{-8 < X<-2} of the solutions