Final answer:
To solve for x in the given polynomial expressions, we combine like terms. The resulting expression is 6x⁴ + 4x³ + 2x² + 7.
Step-by-step explanation:
The student is asked to find the value of x in the sum of two polynomial expressions. The first step in solving this problem is to combine like terms, that is, to add or subtract terms that have the same power of x. The given expressions are (5x³ - 1 +6x⁴) + (2x² + 8 - x³). We simplify this to 6x⁴ + (5x³ - x³) + 2x² - 1 + 8, which simplifies further to 6x⁴ + 4x³ + 2x² + 7.