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

To solve the equation 8/9(x + 1/2) = 32/3, we'll start by simplifying both sides of the equation.

First, let's simplify the left side of the equation:
8/9(x + 1/2) = (8/9)(x) + (8/9)(1/2)
8/9(x + 1/2) = 8/9x + 4/9

Now the equation is:
8/9x + 4/9 = 32/3

To get rid of the fractions, we'll multiply the entire equation by 9:
(9)(8/9x + 4/9) = (9)(32/3)
8x + 4 = 96/3 = 32

Now the equation is:
8x + 4 = 32

Next, we'll isolate the variable x by moving the constant term to the other side of the equation:
8x = 32 - 4
8x = 28

Finally, we'll solve for x by dividing both sides of the equation by 8:
(8x)/8 = 28/8
x = 3.5

Therefore, the solution to the equation 8/9(x + 1/2) = 32/3 is x = 3.5.

When solving for x?

Apologies for the mistake in my previous response.

To solve for x, we'll start again with the equation: 8/9(x + 1/2) = 32/3

First, let's simplify the left side of the equation:
8/9(x + 1/2) = (8/9)(x) + (8/9)(1/2)
8/9(x + 1/2) = 8/9x + 4/18

Now the equation is:
8/9x + 4/18 = 32/3

To simplify the fraction, let's find a common denominator for the right side:
8/9x + 4/18 = (32/3) * (6/6)
8/9x + 4/18 = 192/18

Now the equation is:
8/9x + 4/18 = 192/18

To get rid of the fractions, we'll multiply the entire equation by 18:
(18)(8/9x + 4/18) = (18)(192/18)
(16/9)x + 4 = 192

Now the equation is:
(16/9)x + 4 = 192

Next, we'll isolate the variable x by moving the constant term to the other side of the equation:
(16/9)x = 192 - 4
(16/9)x = 188

Finally, we'll solve for x by multiplying both sides of the equation by (9/16):
((16/9)x)(9/16) = (188)(9/16)
x = (1692/144)
x = 11.75

Therefore, the solution to the equation 8/9(x + 1/2) = 32/3 is x = 11.75.