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

Answer 1

To solve the equation 8/9(x + 1/2) = 32/3 for x, we can start by simplifying the left side of the equation.

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

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

This becomes:

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

Next, combine the fractions on the left side:

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

To solve for x, we can cross multiply:

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

Multiply both sides of the equation:

24x + 12 = 288

Next, isolate the term with x:

24x = 288 - 12

24x = 276

Finally, divide both sides by 24 to solve for x:

x = 276/24

Simplifying the fraction 276/24:

x = 23/2

Therefore, the solution for x is x = 23/2.

Answer 2

8/9(x + 1/2) = 32/3
8 (x+1/2) = 3 * 32 = 96
x + 1/2 = 12
z = 11 1/2

Answer 3

Apologies for the previous response, there appears to be a mistake. Let's go through the solution again:

To solve the equation (8/9)(x + 1/2) = 32/3 for x, follow these steps:

Step 1: Distribute the 8/9 to the terms inside the parentheses.
(8/9)(x) + (8/9)(1/2) = 32/3

This simplifies to:
8/9 * x + 4/9 = 32/3

Step 2: Multiply both sides of the equation by the reciprocal of 8/9, which is 9/8, to eliminate the fraction.
(9/8)(8/9 * x + 4/9) = (9/8)(32/3)

This simplifies to:
x + (9/8)(4/9) = (9/8)(32/3)

Step 3: Simplify both sides of the equation.
x + 4/8 = 12/1

This can be further simplified to:
x + 1/2 = 12

Step 4: To solve for x, subtract 1/2 from both sides.
x + 1/2 - 1/2 = 12 - 1/2

This simplifies to:
x = 11 1/2

Therefore, the solution for x in the equation (8/9)(x + 1/2) = 32/3 is x = 11 1/2 or x = 23/2.