The difference between the areas of the figures is less than 4. An absolute value inequality that represents this situation is ___

The solution of the inequality is ___

Thank you

We know that:

If T = area of the triangle

and R = area of the rectangle:

I T - RI < 4.

Now, we know that:

T = 8*6/2 = 8*3 = 24

R = 4*(x - 4) = 4*x - 16

Then replacing those values, we can write:

I24 - (4*x - 16)I < 4

I40 - 4*xI < 4

Now let's solve it:

First we aim for the first value that is not a solutions, this is when:

I40 - 4*xI = 4

we can write this as:

40 - 4*x = +-4

The first extreme is:

40 - 4*x = +4

x = (40 - 4)/4 = 9

The other extreme is:

40 - 4*x = -4

x = (40 + 4)/4 = 11.

Then the set of solutions is: S = (9, 11)

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