# Math

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Solve the inequality and write the solution set in interval notation
4x^3 -6x^2<0
2x^2 (2x-3)<0

2x-3<0
x= 3/2

2x^2<0
x^2<1/2
sq root of x^2<sq root of 1/2
x=.7071
Right?

When I plug it in the calculator it says
X=0

How?

• Math -

4x^3 - 6x^2 < 0
2x^2 (2x-3) < 0
You should know the general shape of this graph. It has a double root at x=0 and it crosses the x-axis at x=3/2.
So, the graph is below the x-axis for all values of x less than 3/2, except x=0.

2x-3 < 0 is an inequality.
You cannot change it to an equation: x = 3/2

2x-3 < 0
2x < 3
x < 3/2
--------------------------------------

If 2x^2 < 0
you cannot say x^2 < 1/2

0/2 = 0

HINT: x^2 is always >=0, so 2x^2 is always >= 0.
Always

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