Solve the equation for a: (x)/(5)+(2)/(3)=(x)/(9) Write your answer as a fraction. x=square

To solve the equation for x, we need to isolate x on one side of the equation.<br /><br />Given equation: $\frac{x}{5} + \frac{2}{3} = \frac{x}{9}$<br /><br />Step 1: Subtract $\frac{x}{9}$ from both sides of the equation to get:<br />$\frac{x}{5} + \frac{2}{3} - \frac{x}{9} = 0$<br /><br />Step 2: Find a common denominator for the fractions on the left side of the equation. The common denominator is 45.<br /><br />$\frac{9x}{45} + \frac{30}{45} - \frac{5x}{45} = 0$<br /><br />Step 3: Combine the fractions on the left side of the equation:<br />$\frac{9x + 30 - 5x}{45} = 0$<br /><br />Step 4: Simplify the numerator:<br />$\frac{4x + 30}{45} = 0$<br /><br />Step 5: Since the denominator is not zero, we can multiply both sides of the equation by 45 to eliminate the denominator:<br />$4x + 30 = 0$<br /><br />Step 6: Subtract 30 from both sides of the equation:<br />$4x = -30$<br /><br />Step 7: Divide both sides of the equation by 4 to solve for x:<br />$x = -\frac{30}{4} = -\frac{15}{2}$<br /><br />Therefore, the solution to the equation is $x = -\frac{15}{2}$.