Solve the Fraction Equation: Finding X in (6-x)/7 = 3(x-8)/9

Let's solve the equation $\frac{6-x}{7} = \frac{(x-8)\times3}{9}$ step by step:

• Step 1: Cross-multiply to eliminate the fractions:

We have:

$(6-x) \times 9 = ((x-8) \times 3) \times 7$

• Step 2: Expand both sides:

Expanding both products gives:

$9(6-x) = 7 \cdot 3(x-8)$

This simplifies to:

$54 - 9x = 21(x-8)$

• Step 3: Expand the right side and simplify:

Expanding the right side gives:

$54 - 9x = 21x - 168$

• Step 4: Rearrange terms to solve for $x$:

Bring the terms involving $x$ to one side by adding $9x$ to both sides:

$54 = 30x - 168$

Add 168 to both sides to isolate terms involving $x$:

$222 = 30x$

• Step 5: Solve for $x$:

Divide both sides by 30 to find $x$:

$x = \frac{222}{30} = 7.4$

Therefore, the solution to the equation is $x = 7.4$.