if a-p-b,and if ap=2x-9,ab=32,andpb=1.5x=6 then find pb

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The information provided by the problem is incomplete since, `a-p-b` is not given, hence, considering only the given conditions, you may evaluate `x` such that:

`ap=2x-9 => p = (2x-9)/a`

`ab=32 => b = 32/a`

`pb=1.5x + 6`

Substituting `32/a` for `b` and `(2x-9)/a` for `p` yields:

`(32/a)*(2x-9)/a = 1.5x + 6`

`32(2x - 9) = a^2(1.5x + 6)`

`64x - 288 = 1.5xa^2 + 6a^2`

Isolating the terms that contain `x` to the left side yields:

`64x - 1.5xa^2 = 288 + 6a^2`

You need to factor out x such that:

`x(64 - 1.5a^2) = 288 + 6a^2 => x = (288 + 6a^2)/(64 - 1.5a^2)`

Hence, evaluating x you may find the products `ap` and `pb` .

**Notice that the evaluation of `x` , under the given conditions, depends on the variable a such that `x = (288 + 6a^2)/(64 - 1.5a^2).` **

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