Question

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

Answer 1

To solve the equation \( \frac{8}{9}(x + \frac{1}{2}) = \frac{32}{3} \), we can start by eliminating the fraction on the left side by multiplying both sides of the equation by \( \frac{9}{8} \):

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

Calculating the right side:

\[
\frac{32}{3} \cdot \frac{9}{8} = \frac{32 \cdot 9}{3 \cdot 8} = \frac{288}{24} = 12
\]

Thus, we have:

\[
x + \frac{1}{2} = 12
\]

Next, we need to isolate \( x \). We can do this by subtracting \( \frac{1}{2} \) from both sides:

\[
x = 12 - \frac{1}{2}
\]

To subtract, we can convert \( 12 \) to a fraction with a denominator of 2:

\[
12 = \frac{24}{2}
\]

Then, we have:

\[
x = \frac{24}{2} - \frac{1}{2} = \frac{24 - 1}{2} = \frac{23}{2}
\]

Therefore, the solution is:

\[
\boxed{\frac{23}{2}}
\]