what is the solution of the equation 8/9(x+1/2) =32/3

Answer 1

To solve this equation, you can follow these steps:

1. Distribute the 8/9 to both terms inside the parentheses:
(8/9) * x + (8/9) * (1/2) = 32/3

This simplifies to:
(8/9) * x + 4/9 = 32/3

2. Next, subtract 4/9 from both sides of the equation:
(8/9) * x = 32/3 - 4/9

This simplifies to:
(8/9) * x = (32/3) - (4/9)
(8/9) * x = 96/9 - 4/9
(8/9) * x = 92/9

3. Now, multiply both sides of the equation by the reciprocal of 8/9, which is 9/8:
((9/8) * (8/9)) * x = (92/9) * (9/8)

This simplifies to:
x = (92/9) * (9/8)
x = 92/8

4. To simplify the answer, you can also express 92/8 as a mixed number or decimal:
x = 11 2/8 or x = 11.25