Question

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

Answer 1

To solve for x, we need to isolate it on one side of the equation.

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

First, we can distribute 8/9 to both terms inside the parentheses:

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

Next, we simplify:

(8/9)x + 4/9 = 32/3

To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of the denominators, which is 9:

9 * [(8/9)x + 4/9] = 9 * (32/3)

This results in:

8x + 4 = 96/3

Simplifying further:

8x + 4 = 32

Next, we can subtract 4 from both sides of the equation:

8x + 4 - 4 = 32 - 4

This leads to:

8x = 28

To solve for x, we divide both sides of the equation by 8:

(8x)/8 = 28/8

Simplifying further:

x = 7/2

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