Final answer:
The solution to the equation x(3 + x) = 3x + x² involves an infinite number of solutions as the equation simplifies to the same form on both sides. It can be described in words as all real numbers, represented in set notation as x or ℝ, and graphically as two coinciding parabolas for all x values.
Step-by-step explanation:
To solve the equation x(3 + x) = 3x + x², we can expand the left side of the equation to get 3x + x² which simplifies to the right side of the equation; thus, the equation is essentially 3x + x² = 3x + x². This means that the equation is true for all values of x, leading to an infinite number of solutions. Therefore:
- Words: The solution set contains all real numbers because the equation is true for any value of x.
- Set Notation: The solution set can be represented as x or simply as ℝ, which is the symbol for the set of all real numbers.
- Graphically: A graphical representation would show the two identical parabolas y = 3x + x² and y = x(3 + x) coinciding with each other for all values of x on the Cartesian plane.
Thus, the correct representation for the solution set would involve D) All of the above options: describing in words, using set notations, and showing graphically.