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 for x, we can begin by simplifying both sides of the equation.

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

Now we have the equation:
(8/9)x + 4/9 = 32/3

Next, we can get rid of the fraction by multiplying every term in the equation by 9, to cancel out the denominators:
9 * ((8/9)x + 4/9) = 9 * (32/3)
8x + 4 = 96/3

Simplifying the right side:
8x + 4 = 32

To isolate the variable, we can subtract 4 from both sides of the equation:
8x + 4 - 4 = 32 - 4
8x = 28

Finally, to solve for x, we divide both sides by 8:
(8x)/8 = 28/8
x = 7/2

Therefore, the solution to the equation 8/9(x+1/2) = 32/3 when solving for x is x = 7/2.