Solve for X: Finding the Value in -1/3x + 5 = 6/9x

To solve this problem, we'll follow these steps:

• Step 1: Manipulate the equation to consolidate terms involving $x$.
• Step 2: Simplify the equation by fixing fractions.
• Step 3: Solve for $x$ to find the solution.

Now, let's work through each step:
Step 1: Start with the original equation, $-\frac{1}{3}x + 5 = \frac{6}{9}x$. First, simplify $\frac{6}{9}$ to $\frac{2}{3}$, giving us the equivalent equation:
$-\frac{1}{3}x + 5 = \frac{2}{3}x.$

Step 2: Move the $-\frac{1}{3}x$ term to the right side to consolidate terms,
$5 = \frac{2}{3}x + \frac{1}{3}x.$

Step 3: Simplify the terms involving $x$ on the right side. $\frac{2}{3}x + \frac{1}{3}x = \frac{3}{3}x = x.$ Thus, the equation becomes:
$5 = x.$

Therefore, the solution to the equation is $x = 5$.