(x:2)-10=x:3

To solve the equation \((x:2) - 10 = x:3\), we can rewrite it without using the colon notation: Let \(x:2\) denote \(\frac{x}{2}\) and \(x:3\) denote \(\frac{x}{3}\). The equation then becomes: \[ \frac{x}{2} - 10 = \frac{x}{3} \] Now, to eliminate the fractions, we can find a common denominator. The least common multiple of \(2\) and \(3\) is \(6\). We'll multiply every term by \(6\): \[ 6 \left(\frac{x}{2}\right) - 6(10) = 6 \left(\frac{x}{3}\right) \] This simplifies to: \[ 3x - 60 = 2x \] Now, we will isolate \(x\) by subtracting \(2x\) from both sides: \[ 3x - 2x - 60 = 0 \] Which simplifies to: \[ x - 60 = 0 \] Now, add \(60\) to both sides: \[ x = 60 \] Thus, the solution to the equation is: \[ \boxed{60} \]