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

Question

when solving for x
?(1 point)
x = ___

Answer 1

To solve the equation \( \frac{8}{9}\left(x + \frac{1}{2}\right) = \frac{32}{3} \), follow these steps:

1. Multiply both sides by 9 to eliminate the fraction:

   \[ 9 \cdot \frac{8}{9}\left(x + \frac{1}{2}\right) = 9 \cdot \frac{32}{3} \]

   This simplifies to:

   \[ 8\left(x + \frac{1}{2}\right) = 96 \]

2. Distribute the 8 on the left side:

   \[ 8x + 4 = 96 \]

3. Subtract 4 from both sides:

   \[ 8x = 96 - 4 \]

   So,

   \[ 8x = 92 \]

4. Divide both sides by 8:

   \[ x = \frac{92}{8} \]

   Simplify the fraction:

   \[ x = \frac{23}{2} \quad \text{or} \quad x = 11.5 \]

Thus, the solution for \( x \) is:

\[ x = \frac{23}{2} \] or \( x = 11.5 \).