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

Answer 1

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

Given: $\frac{8}{9}(x+\frac{1}{2}) = \frac{32}{3}$

First, we can distribute the $\frac{8}{9}$ to both terms inside the parentheses:

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

This simplifies to:

$\frac{8x}{9} + \frac{4}{9} = \frac{32}{3}$

Next, we can subtract $\frac{4}{9}$ from both sides of the equation to get rid of it from the left side:

$\frac{8x}{9} = \frac{32}{3} - \frac{4}{9}$

Simplifying the right side:

$\frac{8x}{9} = \frac{32 \cdot 3}{3} - \frac{4}{9}$

$\frac{8x}{9} = \frac{96}{3} - \frac{4}{9}$

$\frac{8x}{9} = \frac{92}{9}$

To isolate x, we can multiply both sides of the equation by the reciprocal of $\frac{8}{9}$, which is $\frac{9}{8}$:

$\frac{9}{8} \cdot \frac{8x}{9} = \frac{9}{8} \cdot \frac{92}{9}$

This simplifies to:

$x = \frac{828}{72}$

Simplifying further, we get:

$x = \frac{69}{6}$

Therefore, the solution to the equation is $x = \frac{69}{6}$.