Solve for X in (3-x)/9 = (4+x)/6: Fraction Equation Practice

To solve the equation $\frac{3-x}{9} = \frac{4+x}{6}$, we will use the method of cross-multiplication to eliminate the fractions.

Step 1: Cross-multiply to get rid of the fractions. This involves multiplying the numerator of each fraction by the denominator of the other:

$(3-x) \times 6 = (4+x) \times 9$

Step 2: Distribute the multiplication over the terms inside the parentheses:

$6(3-x) = 9(4+x)$

$18 - 6x = 36 + 9x$

Step 3: Combine like terms to simplify the equation. Start by getting all the $x$-terms on one side and the constant terms on the other:

• Add $6x$ to both sides: $18 = 36 + 9x + 6x$
• Rearrange: $18 = 36 + 15x$
• Subtract 36 from both sides: $18 - 36 = 15x$
• Result: $-18 = 15x$

Step 4: Solve for $x$ by dividing both sides by 15:

$x = \frac{-18}{15}$

Therefore, the solution to the equation is $x = -\frac{18}{15}$.