Final answer:
The sentence 'When one is subtracted from three times a number p, the result is eight less than six times the original number' translates into the equation 3p - 1 = 6p - 8, representing the relationship described in the sentence.
Step-by-step explanation:
The sentence 'When one is subtracted from three times a number p, the result is eight less than six times the original number' can be translated into symbols as follows:
Firstly, let's consider 'three times a number p'. This can be represented by 3p. The phrase 'when one is subtracted from' indicates that we should subtract 1 from the result of three times p, so we get 3p - 1.
Next, the phrase 'the result is eight less than six times the original number' translates to the result being equal to 6p - 8. This is because 'eight less than' indicates subtraction after multiplying the number p by six.
Finally, combining these two parts into one equation, we get:
3p - 1 = 6p - 8
This is the symbolic representation of the given sentence.