Final answer:
The equivalent expression to 4/5(1 1/4x + 3 1/3) is x + 2 2/3 after distributing 4/5 across the terms and simplifying the fractions.
Step-by-step explanation:
To find which expression is equivalent to 4/5(1 1/4x + 3 1/3), we first need to simplify and distribute the fraction 4/5 across the terms inside the parenthesis. We start by converting mixed numbers to improper fractions. So, 1 1/4 becomes 5/4, and 3 1/3 becomes 10/3.
Now, we multiply 4/5 by each of the improper fractions:
4/5 * 5/4x = (4*5)/(5*4)x = 1x = x
4/5 * 10/3 = (4*10)/(5*3) = 40/15 = 8/3 = 2 2/3
Putting it all together, we get x + 2 2/3, which means the correct answer is option B: x+ 2 2/3.