Himpunan penyelesaian pertidaksamaan nilai mutlak |2x-4| > |3x+2|

The solution in interval notation is:

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The solution in inequality notation is:

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Step-by-step explanation:

I think you are asking how to solve this for .

Keep in mind .

If then .

Subtract on both sides:

Factor the difference of squares :

Simplify inside the factors:

The left hand side is a parabola that faces up.  I know this because the degree is 2.  

The zeros of the the parabola are at x=-6 and x=2/5.

We can solve x+6=0 and 5x-2=0 to reach that conclusion.

x+6=0

Subtract 6 on both sides:

x=-6

5x-2=0

Add 2 on both sides:

5x=2

Divide both sides by 5:

x=2/5

Since the parabola faces us and then we are looking at the interval from x=-6 to x=2/5 as our solution.  That part is where the parabola is below the x-axis.  We are looking for where it is below since it says the where is the parabola<0.

The solution in interval notation is:

.

The solution in inequality notation is:

.