Question

completwe the factoring if needed and solve the polynomial ineqaulity using a sign chart

(2x+1)(x-2)(3x-4)≤0

Answer 1

2x+1)(x-2)(3x-4)<=0
it can be written as
(x+1/2)(x-2)(x-4/3)<=0
we have on the number line

Answer 2

Your the best !

Answer 3

wait i'm solving

Answer 4

there are four ranges of interest
a)x <=-1/2
b)-1/2<=x<=4/3
c) 4/3<=x<=2
d) x>=2

let's check the inequality for each range
(x+1/2)(x-4/3)(x-2)
a) when x<=-1/2
let's say x=-1
then (-1+1/2)(-1-4/3)(-1-2)
-21/6 this is less than equal to 0 , so this is a part of our solution
b) -1/2<=x<=4/3
let x = 1
then (1+1/2)(1-4/3)(1-2)
1/2 is not less than or equal to zero
so this is not of our interest
c) 4/3<=x<=2
let x be 3/2
(3/2+1/2)(3/2-4/3)(3/2-2)
-1/6 <=0
this is a part of our solution
d) when x>=2
if you evaluate it's positive
son not of our interest
so our solution is x<=-1/2 and 4/3<=x<=2