Final answer:
To solve the equation with a fractional coefficient, we convert mixed numbers to improper fractions. A comparison of the coefficients on both sides of the equation reveals a typographical mistake in the question, as it results in x equating to 5/8, which is not offered as an option.
Step-by-step explanation:
To solve the equation 2 1/3 x 5/8 = 2 1/3 10/16, we first recognize that the equation is not balanced because the two sides of the equation represent different values. The value of x is the unknown we need to find. By observing that 10/16 can be simplified to 5/8, we identify a mistake in the formation of the equation. To find x, we should solve the correct equation, which is 2 1/3 x 5/8 = 2 1/3 * 5/8.
First, convert the mixed number 2 1/3 to an improper fraction: 2 1/3 = (2*3 + 1)/3 = 7/3.
Next, we rewrite the equation as 7/3 * x = 7/3 * 5/8. Since the coefficients on each side of the equation are the same, it means that x must be equal to 5/8 for the equation to hold true.
Therefore, x = 5/8 which is not one of the given options, suggesting a possible typo or error in the question.