To solve the equation 8/9(x + 1/2) = 32/3 for x, we can begin by simplifying:
8/9(x + 1/2) = 32/3
Next, we distribute the 8/9 to both terms inside the parentheses:
(8/9)(x) + (8/9)(1/2) = 32/3
Now we can simplify the equation further by multiplying:
8x/9 + 4/9 = 32/3
To get rid of the denominators, we can multiply both sides of the equation by 9:
9(8x/9 + 4/9) = 9(32/3)
This simplifies to:
8x + 4 = 96/3
8x + 4 = 32
Subtracting 4 from both sides of the equation:
8x = 32 - 4
8x = 28
Finally, divide both sides of the equation by 8:
x = 28/8
x = 7/2
Therefore, the solution to the equation is x = 7/2.