Solve the Fraction Equation: Balance −8 + X/3 = X + 4/9

To solve for $x$ in the equation $\frac{-8+x}{3}=\frac{x+4}{9}$, we'll follow these steps:

• Step 1: Eliminate the fractions by finding a common denominator.
• Step 2: Simplify the resulting equation.
• Step 3: Isolate $x$ to solve the equation.

Let's proceed step by step:

Step 1: The equation $\frac{-8+x}{3}=\frac{x+4}{9}$ contains denominators 3 and 9. The least common denominator (LCD) is 9. To eliminate the fractions, multiply every term of the equation by 9.

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

Simplifying, we have:

$3(-8 + x) = x + 4$

Step 2: Distribute the 3 on the left side:

$3 \times -8 + 3 \times x = x + 4$

This simplifies to:

$-24 + 3x = x + 4$

Step 3: Isolate $x$. First, subtract $x$ from both sides of the equation:

$-24 + 3x - x = x + 4 - x$

This simplifies to:

$-24 + 2x = 4$

Next, add 24 to both sides to further isolate $x$:

$-24 + 24 + 2x = 4 + 24$

This simplifies to:

$2x = 28$

Finally, divide both sides by 2 to solve for $x$:

$x = \frac{28}{2}$

Simplifying this gives:

$x = 14$

Therefore, the solution to the equation is $x = 14$.