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# 6x^3 - 9x^2<0

6x3 - 9x<0
Solving for all values of x.

### 3 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
1
6x^3 - 9x^2 < 0

6x^2(x - 3/2) < 0

Left side has zeros at 0 and 3/2.

Left side is negative when x ≠ 0 and x < 3/2;

i.e., x ∈ (–∞,0) U (0,3/2).
Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
4.9 4.9 (418 lesson ratings) (418)
0
6x3 - 9x2 < 0

3x2(2x - 3) < 0

The 3x2 term is always positive, so we must have:

(2x - 3) < 0

2x < 3

x < 3/2

On a number line, put a circle at x = 3/2 to indicate that 3/2 is not in the solution set, then darken in all values of x < 3/2.

check x = 0 in original equation
Jim S. | Physics (and math) are fun, reallyPhysics (and math) are fun, really
4.7 4.7 (175 lesson ratings) (175)
0
Hi Cyn',
You can write the inequality, by factoring out 3x2, as follows

3x2(2x-3)<0  by inspection the roots are x=0 and x=3/2. so for x<0 the inequality is satisfied because 2x-3 <0 when x<0 and the inequality is satisfied when 0<x<3/2. When x>3/2 the function is positive so the inequality is not satisfied.

Jim