Final answer:
To find the value of b - a, simplify the equation and compare the coefficients of the x terms. The value of b - a is 19.
Step-by-step explanation:
To find the value of b - a, we need to simplify the given equation and compare the coefficients of the x terms.
Start by expanding the expression:
8x² - 150 - 22 + 27x = ax² + bx
Combine like terms:
8x² + 27x - 172 = ax² + bx
Since the equation is true for all values of x, the coefficients of the x terms on both sides should be equal.
Comparing the coefficients, we have:
8x² + 27x - 172 = ax² + bx
8 = a, 27 = b
Therefore, the value of b - a is 27 - 8 = 19.