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

Answer 1

To solve for x in the equation 8/9(x + 1/2) = 32/3, first distribute 8/9 to both terms inside the parentheses:

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

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

Next, subtract 4/9 from both sides:

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

To add the fractions, find a common denominator, which in this case is 9:

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

This simplifies to:

8/9(x) = 288/9 - 4/9

8/9(x) = 284/9

To isolate x, multiply both sides of the equation by the reciprocal of 8/9, which is 9/8:

(9/8)(8/9)(x) = (9/8)(284/9)

This simplifies to:

x = 284/8

To further simplify, divide both the numerator and denominator by their greatest common divisor, which is 4:

x = (71/2)(1/4)

The solution for x is:

x = 71/8