Question

\frac{2-x}{3} - \frac{6-x}{2} = 0

Answer 1

$\frac{2-x}{3}-\frac{6-x}{2}=0$
$2*(2-x)-3*(6-x)=0$
$4-2x-18+3x=0$
$-14+x=0$
$x=14$

Answer 2

To solve the equation $\frac{{2-x}}{3} - \frac{{6-x}}{2} = 0$, we can simplify and solve for $x$:

Step 1: Multiply through by the common denominator of 3 and 2, which is 6, to eliminate the fractions: $2 \cdot 2 \cdot (2-x) - 3 \cdot 3 \cdot (6-x) = 0$

Step 2: Distribute the multiplication: $4(2-x) - 9(6-x) = 0$

Step 3: Simplify the expressions: $8 - 4x - 54 + 9x = 0$

Step 4: Combine like terms: $-45 + 5x = 0$

Step 5: Move the constant term to the other side: $5x = 45$

Step 6: Divide both sides by 5: $x = \frac{45}{5} = 9$

Therefore, the solution to the equation is $x = 9$.