What is the solution of the equation 8/9 (x+1/2) =32/3 when solving for x?

Answer 1

To solve the equation:

8/9(x + 1/2) = 32/3

First, we can simplify both sides of the equation.

On the left side, we distribute 8/9 to (x + 1/2):

8/9 * x + 8/9 * 1/2 = 32/3

8/9 * x + 4/9 = 32/3

Now, let's isolate the term with x by subtracting 4/9 from both sides:

8/9 * x = 32/3 - 4/9

8/9 * x = 96/9 - 4/9

8/9 * x = 92/9

To get x by itself, we can multiply both sides of the equation by the reciprocal of 8/9, which is 9/8:

(8/9 * x) * (9/8) = (92/9) * (9/8)

x = 92/8

To simplify x, we can write 92/8 as a mixed number:

x = 11 4/8

And converting the mixed number to a simplified fraction:

x = 11 1/2

Therefore, the solution to the equation 8/9(x + 1/2) = 32/3 is x = 11 1/2.